Publications on ArXiv

Measuring fluctuations in matter's low energy excitations is the key to unveil the nature of the nonequilibrium response of materials. A promising outlook in this respect is offered by spectroscopic methods that address matter fluctuations by exploiting the statistical nature of light-matter interactions with weak few-photon probes. Here we report the first implementation of ultrafast phase randomized tomography, combining pump-probe experiments with quantum optical state tomography, to measure the ultrafast non-equilibrium dynamics in complex materials. Our approach utilizes a time-resolved multimode heterodyne detection scheme with phase-randomized coherent ultrashort laser pulses, overcoming the limitations of phase-stable configurations and enabling a robust reconstruction of the statistical distribution of phase-averaged optical observables. This methodology is validated by measuring the coherent phonon response in $\alpha$-quartz. By tracking the dynamics of the shot-noise limited photon number distribution of few-photon probes with ultrafast resolution, our results set an upper limit to the non-classical features of phononic state in $\alpha$-quartz and provide a pathway to access nonequilibrium quantum fluctuations in more complex quantum materials.

We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the Bose-Hubbard (BH) and sine-Gordon (SG) regimes. While in higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in 1D an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the SG model. The present work aims at identifying the SG and BH regimes. We study them by dynamical measures of several key quantities. We numerically exactly solve the time dependent Schr\"odinger equation for small number of atoms and investigate the corresponding quantum many-body dynamics. In both cases, correlation dynamics exhibits collapse revival phenomena, though with different time scales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics specially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. BH dynamics clearly establishes the possible relaxation to the maximum entropy state determined by the Gaussian orthogonal ensemble of random matrices (GOE). In contrast, the SG dynamics is so fast that it does not exhibit any signature of relaxation in the present time scale of computation.

Impurities immersed in hard-core Bose gases offer exciting opportunities to explore polaron and bipolaron physics. We investigate the ground state properties of a single and a pair of impurities throughout the superfluid and insulating (charge density wave) phases of the bosonic environment. In the superfluid phase, we demonstrate that the impurity undergoes a polaron-like transition, shifting from behaving as an individual particle to becoming a dressed quasiparticle as the coupling with the bath increases. However, in the insulating phase, the impurity can maintain its individual character, moving through a potential landscape shaped by the charge density wave order. Moreover, we show that two impurities can form a bound state even in the absence of an explicit impurity-impurity coupling. Furthermore, we establish the stability of this bound state within both the superfluid and insulating phases. Our results offer valuable insights for ongoing lattice polaron experiments with ultracold gases.

The surface ligands in colloidal metal halide perovskites influence not only their intrinsic optoelectronic properties but also their interaction with other materials and molecules. We explore donor-acceptor interactions of CsPbBr3 perovskite nanocrystals with TiO2 nanoparticles and nanotubes by replacing long-chain oleylamine ligands with short-chain butylamines. Through post-synthesis ligand exchange, we functionalize the nanocrystals with butylamine ligands while maintaining their intrinsic properties. In solution, butylamine-capped nanocrystals exhibit reduced photoluminescence intensity with increasing TiO2 concentration but without any change in photoluminescence lifetime. Intriguingly, the Stern-Volmer plot depicts different slopes at low and high TiO2 concentrations, suggesting mixed static and sphere-of-action quenching interactions. Oleylamine-capped nanocrystals in solution, on the other hand, show no interaction with TiO2, as indicated by consistent photoluminescence intensities and lifetimes before and after TiO2 addition. In films, both types exhibit decreased photoluminescence lifetime with TiO2, indicating enhanced donor-acceptor interactions, which are discussed in terms of trap state modification and electron transfer. TiO2 nanotubes enhance nonradiative recombination more in butylamine-capped CsPbBr3 perovskite nanocrystals, emphasizing the role of ligand chain length.

The $U(1)$ Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in $2+1$ dimensions, where gapless modes exists but spinons and gauge fields are strongly coupled. Its existence has been proposed in frustrated Heisenberg models in presence of frustrating super-exchange interactions, by the (Abrikosov) fermionic representation of the spin operators [X.-G. Wen, Phys. Rev. B 65, 165113 (2002)}], supplemented by the Gutzwiller projection. Here, we construct charge-$Q$ monopole excitations in the Heisenberg model on the triangular lattice with nearest- ($J_1$) and next-neighbor ($J_2$) couplings. In the highly frustrated regime, singlet and triplet monopoles with $Q=1$ become gapless in the thermodynamic limit; in addition, the energies for generic $Q$ agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $\pi$-fluxes are concentrated in the triangular plaquettes (in analogy with $\mathbb{Z}_2$ visons), showing that these kind of states do not play a relevant role at low-energies. All our findings lend support to a stable $U(1)$ Dirac spin liquid in the $J_1-J_2$ Heisenberg model on the triangular lattice.

We analyze the performance of the Harrow-Hassidim-Lloyd algorithm (HHL algorithm) for solving linear problems and of a variant of this algorithm (HHL variant) commonly encountered in literature. This variant relieves the algorithm of preparing an entangled initial state of an auxiliary register. We prove that the computational error of the variant algorithm does not always converge to zero when the number of qubits is increased, unlike the original HHL algorithm. Both algorithms rely upon two fundamental quantum algorithms, the quantum phase estimation and the amplitude amplification. In particular, the error of the HHL variant oscillates due to the presence of undesired phases in the amplitude to be amplified, while these oscillations are suppressed in the original HHL algorithm. Then, we propose a modification of the HHL variant, by amplifying an amplitude of the state vector that does not exhibit the above destructive interference. We also study the complexity of these algorithms in the light of recent results on simulation of unitaries used in the quantum phase estimation step, and show that the modified algorithm has smaller error and lower complexity than the HHL variant. We supported our findings with numerical simulations.

We study families of deformed ADE surfaces by probing them with a D2-brane in Type IIA string theory. The geometry of the total space $X$ of such a family can be encoded in a scalar field $\Phi$, which lives in the corresponding ADE algebra and depends on the deformation parameters. The superpotential of the probe three dimensional (3d) theory incorporates a term that depends on the field $\Phi$. By varying the parameters on which $\Phi$ depends, one generates a family of 3d theories whose moduli space always includes a geometric branch, isomorphic to the deformed surface. By fibering this geometric branch over the parameter space, the total space $X$ of the family of ADE surfaces is reconstructed. We explore various cases, including when $X$ is the universal flop of length $\ell=1,2$. The effective theory, obtained after the introduction of $\Phi$, provides valuable insights into the geometric features of $X$, such as the loci in parameter space where the fiber becomes singular and, more notably, the conditions under which this induces a singularity in the total space. By analyzing the monopole operators in the 3d theory, we determine the charges of certain M2-brane states arising in M-theory compactifications on $X$.

M-theory geometric engineering on non-compact Calabi-Yau fourfolds (CY4) produces 3d theories with 4 supercharges. Carefully establishing a dictionary between the geometry of the CY4 and the QFT in the transverse directions remains, to a large extent, an unresolved challenge, complicated by subtleties arising from M5-brane instanton corrections. Such difficulties can be circumvented in the restricted and yet controlled setting offered by CY4 with terminal singularities, as they do not admit crepant resolutions with compact exceptional divisors. After a general review of their properties and partial classifications, we focus on a subclass of terminal CY4 constructed as deformed Du Val singularities, that admit crepant resolutions with at most exceptional 2-cycles. We extract the corresponding 3d $\mathcal{N}=2$ supersymmetric theory descendant in an unambiguous fashion, as the absence of compact 4-cycles leaves no room for a choice of background $G_4$ flux. These turn out to be theories of chiral multiplets with no gauge group and at most abelian flavor factors: we argue that they serve as the simplest building blocks to substantiate a rigorous CY4/3d QFT geometric engineering mapping.

This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate (BEC) of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fr\"ohlich Hamiltonian that applies at weak couplings. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.

Variational quantum computing provides a versatile computational approach, applicable to a wide range of fields such as quantum chemistry, machine learning, and optimization problems. However, scaling up the optimization of quantum circuits encounters a significant hurdle due to the exponential concentration of the loss function, often dubbed the barren plateau (BP) phenomenon. Although rigorous results exist on the extent of barren plateaus in unitary or in noisy circuits, little is known about the interaction between these two effects, mainly because the loss concentration in noisy parameterized quantum circuits (PQCs) cannot be adequately described using the standard Lie algebraic formalism used in the unitary case. In this work, we introduce a new analytical formulation based on non-negative matrix theory that enables precise calculation of the variance in deep PQCs, which allows investigating the complex and rich interplay between unitary dynamics and noise. In particular, we show the emergence of a noise-induced absorption mechanism, a phenomenon that cannot arise in the purely reversible context of unitary quantum computing. Despite the challenges, general lower bounds on the variance of deep PQCs can still be established by appropriately slowing down speed of convergence to the deep circuit limit, effectively mimicking the behaviour of shallow circuits. Our framework applies to both unitary and non-unitary dynamics, allowing us to establish a deeper connection between the noise resilience of PQCs and the potential to enhance their expressive power through smart initialization strategies. Theoretical developments are supported by numerical examples and related applications.

In this note we study nonequilibrium fluctuations in gravitational algebras within de Sitter space. An essential aspect of this study is quantum measurement theory, which allows us to access the dynamical fluctuations of observables via a two-point measurement scheme. Using this formalism, we establish specific fluctuation theorems. Additionally, we demonstrate that quantum channels are represented by subfactors, using the relationship between measurement theory and quantum channels. We also comment on implementing a quantum channel using Jones' theory of subfactors.

The critical behaviour of the classical (thermal) phase transition (CPT) of the Ising model is identical to the quantum phase transition (QPT) of the $\phi^4$ Quantum Field Theory (QFT). Our goal in this work is to map out the QPT-CPT diagram of the $\phi^4$ QFT, and study its relation to the well-known QPT-CPT phase diagram of the Ising model. To do this, we propose a modification of the usual finite-temperature Renormalization Group (RG) approach by relating the temperature parameter to the running RG scale, $T \equiv k_T = \tau k$ where $k_T$ is the running cutoff for thermal, and $k$ is for the quantum fluctuations. In this case, the temperature is related to the dimensionless quantity $\tau$. We apply this new thermal RG approach for the $\phi^4$ model in lower dimensions and construct its QPT-CPT phase diagram. We formulate requirements for the QPT-CPT phase diagram of the $\phi^4$ theory based on known properties of the QPT-CPT phase diagram of the Ising model. Finally, we use these requirements to check the viability of the thermal RG method proposed in this work.

Spontaneous collapse models, which are phenomenological mechanisms introduced and designed to account for dynamical wavepacket reduction, are attracting a growing interest from the community interested in the characterisation of the quantum-to-classical transition. Here, we introduce a {\it quantum-probing} approach to the quest of deriving metrological upper bounds on the free parameters of such empirical models. To illustrate our approach, we consider an extended quantum Ising chain whose elements are -- either individually or collectively -- affected by a mechanism responsible for spontaneous collapse. We explore configurations involving out-of-equilibrium states of the chain, which allows us to infer information about the collapse mechanism before it is completely scrambled from the state of the system. Moreover, we investigate potential amplification effects on the probing performance based on the exploitation of quantum criticality.

We study Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. As observed in [1] this implies a deconfinement-confinement transition as the radius is increased. We gather hints on the nature of this transition using perturbation theory. We compute the anomalous dimensions of the lightest scalar operators in the boundary theory, which are negative for the singlet and positive for non-trivial representations. We also compute the correction to the coefficient $C_J$ and we estimate that the singlet operator reaches marginality before the value of the coupling at which $C_J=0$. These results favor the scenario of merger and annihilation as the most promising candidate for the transition. For the Neumann boundary condition, the lightest scalar operator is found to have a positive anomalous dimension, in agreement with the idea that this boundary condition extrapolates smoothly to flat space. The perturbative calculations are made possible by a drastic simplification of the gauge field propagator in Fried-Yennie gauge. We also derive a general result for the leading-order anomalous dimension of the displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings.

The interplay between electron-electron and electron-phonon interactions is studied in a one-dimensional lattice model, by means of a variational Monte Carlo method based on generalized Jastrow-Slater wave functions. Here, the fermionic part is constructed by a pair-product state, which explicitly depends on the phonon configuration, thus including the electron-phonon coupling in a backflow-inspired way. We report the results for the Hubbard model in presence of the Su-Schrieffer-Heeger coupling to optical phonons, both at half-filling and upon hole doping. At half-filling, the ground state is either a translationally invariant Mott insulator, with gapless spin excitations, or a Peierls insulator, which breaks translations and has fully gapped excitations. Away from half-filling, the charge gap closes in both Mott and Peierls insulators, turning the former into a conventional Luttinger liquid (gapless in all excitation channels). The latter, instead, retains a finite spin gap that closes only above a threshold value of the doping. Even though consistent with the general theory of interacting electrons in one dimension, the existence of such a phase (with gapless charge but gapped spin excitations) has never been demonstrated in a model with repulsive interaction and with only two Fermi points. Since the spin-gapped metal represents the one-dimensional counterpart of a superconductor, our results furnish evidence that a true off-diagonal long-range order may exist in the two-dimensional case.

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed.

The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Di\'osi-Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound $R_0\gtrsim 4 \times 10^{-10}$ m for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: $R_0\lesssim 10^{-4}$ m. This will serve to better direct future experiments to further test the model.

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear nature, which makes them challenging to detect using standard methods. This paper exploits the entanglement between intrinsic dimensionality and correlation to propose a metric that quantifies the (potentially nonlinear) correlation between high-dimensional manifolds. We first validate our method on synthetic data in controlled environments, showcasing its advantages and drawbacks compared to existing techniques. Subsequently, we extend our analysis to large-scale applications in neural network representations. Specifically, we focus on latent representations of multimodal data, uncovering clear correlations between paired visual and textual embeddings, whereas existing methods struggle significantly in detecting similarity. Our results indicate the presence of highly nonlinear correlation patterns between latent manifolds.

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions, which explicitly include spatial correlations and electron pairing. We span the nonmagnetic sector ranging from a filling $n=4$, which is representative of undoped iron-based superconductors, to $n=3$. In the latter case, a Mott insulating state is found, with each orbital at half filling. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of $d_{xz}$ and $d_{yz}$ orbitals, which leads to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half filled for all densities while the other one hosts (together with the $d_{xy}$ orbital) the excess of electron density. Most importantly, in this regime, long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund's coupling.

These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and Quantum Error Mitigation.

We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range couplings which can be either ferromagnetic or antiferromagnetic. Despite the relative simplicity of the model, our calculations in the microcanonical ensemble reveal a rich phase diagram. The comparison with the corresponding phase diagram in the canonical ensemble shows the presence of phase transition points and lines which are different in the two ensembles. As an example, in a region of the phase diagram where the canonical ensemble shows a critical point and a critical end point, the microcanonical ensemble has an additional critical point and also a triple point. The regions of ensemble inequivalence typically occur at lower temperatures and at larger absolute values of the competing couplings. The presence of two free parameters in the model allows us to obtain a fourth-order critical point, which can be fully characterized by deriving its Landau normal form.

We investigate the divisibility properties of the tensor products $\Lambda^{(1)}_t\otimes\Lambda^{(2)}_t$ of open quantum dynamics $\Lambda^{(1,2)}_t$ with time-dependent generators. These dynamical maps emerge from a compound open system $S_1+S_2$ that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to $S_1+S_2$ without the same phenomenon occurring for either $S_1$ and $S_2$. We shall refer to this effect as the Superactivation of BFI (SBFI).

Time-evolution of the Universe as described by the Friedmann equation can be coupled to equations of motion of matter fields. Quantum effects may be incorporated to improve these classical equations of motion by the renormalization group (RG) running of their couplings. Since temporal and thermal evolutions are linked to each other, astrophysical and cosmological treatments based on zero-temperature RG methods require the extension to finite-temperatures. We propose and explore a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale as $T \equiv k_T = \tau k$ (in natural units), where $k_T$ is acting as a running cutoff for thermal fluctuations and the momentum $k$ can be used for the quantum fluctuations. In this approach, the temperature of the expanding Universe is related to the dimensionless quantity $\tau$ (and not to $k_T$). We show that by this choice dimensionless RG flow equations have no explicit $k$-dependence, as it is convenient. We also discuss how this modified thermal RG is used to handle high-energy divergences of the RG running of the cosmological constant and to "solve the triviality"of the $\phi^4$ model by a thermal phase transition in terms of $\tau$ in $d=4$ Euclidean dimensions.

$P$-divisibility is a central concept in both classical and quantum non-Markovian processes; in particular, it is strictly related to the notion of information backflow. When restricted to a fixed commutative algebra generated by a complete set of orthogonal projections, any quantum dynamics naturally provides a classical stochastic process. It is indeed well known that a quantum generator gives rise to a $P$-divisible quantum dynamics if and only if all its possible classical reductions give rise to divisible classical stochastic processes. Yet, this property does not hold if one operates a classical reduction of the quantum dynamical maps instead of their generators: as an example, for a unitary dynamics, $P$-divisibility of its classical reduction is inevitably lost, which thus exhibits information backflow. Instead, for some important classes of purely dissipative qubit evolutions, quantum $P$-divisibility always implies classical $P$-divisibility and thus lack of information backflow both in the quantum and classical scenarios. On the contrary, for a wide class of orthogonally covariant qubit dynamics, we show that loss of classical $P$-divisibility can originate from the classical reduction of a purely dissipative $P$-divisible quantum dynamics as in the unitary case. Moreover, such an effect can be interpreted in terms of information backflow, the information coming in being stored in the coherences of the time-evolving quantum state.

Exchange energy statistics between two bodies at different thermal equilibrium obey the Jarzynski-W\'ojcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a, possibly non-thermal, asymptotic state. To generalize the Jarzynski-W\'ojcik theorem to non-thermal states, we identify a sufficient condition ${\cal I}$ for the existence of an energy scale factor $\eta^{*}$ that is unique, finite and time-independent, such that the characteristic function of the exchange energy distribution becomes identically equal to $1$ for any time. This $\eta^*$ plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition ${\cal I}$, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of ${\cal I}$ is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.

The famous Goldbach conjecture states that any even natural number $N$ greater than $2$ can be written as the sum of two prime numbers $p$ and $p'$, with $p \, , p'$ referred to as a Goldbach pair. In this article we present a quantum analogue protocol for detecting -- given a even number $N$ -- the existence of a so-called minimal Goldbach partition $N=p+p'$ with $p\equiv p_{\rm min}(N)$ being the so-called minimal Goldbach prime, i.e. the least possible value for $p$ among all the Goldbach pairs of $N$. The proposed protocol is effectively a quantum Grover algorithm with a modified final stage. Assuming that an approximate smooth upper bound $\mathcal{N}(N)$ for the number of primes less than or equal to $ p_{\rm min}(N)$ is known, our protocol will identify if the set of $\mathcal{N}(N)$ lowest primes contains the minimal Goldbach prime in approximately $\sqrt{\mathcal{N}(N)}$ steps, against the corresponding classical value $\mathcal{N}(N)$. In the larger context of a search for violations of Goldbach's conjecture, the quantum advantage provided by our scheme appears to be potentially convenient. E.g., referring to the current state-of-art numerical search for violations of the Goldbach conjecture among all even numbers up to $N_{\text{max}} = 4\times 10^{18}$ [T. O. e Silva, S. Herzog, and S. Pardi, Mathematics of Computation 83, 2033 (2013)], a quantum realization of the search would deliver a quantum advantage factor of $\sqrt{\mathcal{N}(N_{\text{max}})} \approx 37$ and it will require a Hilbert space spanning $\mathcal{N}(N_{\text{max}}) \approx 1376$ basis states.

Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We analyze the performance of a scheme that, by embedding careful time-control of trapping potentials and fully accounting for the most relevant sources of noise -- including measurement backaction -- achieves significant levels of mechanical squeezing. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering.

Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is in general true both classically and quantum mechanically. We show, however, that in the context of open quantum systems, two Lagrangians that differ by a total derivative can lead to different physical predictions. We then discuss the criterion that allows one to choose between such Lagrangians. Further, starting from the appropriate QED Lagrangian, we derive the master equation for the non-relativistic electron interacting with thermal photons upto second order in the interactions. This case study lends further phenomenological support to our proposed criterion.

We numerically study the expansion dynamics of initially localized dipolar bosons in a homogeneous 1D optical lattice for different initial states. Comparison is made to interacting bosons with contact interaction. For shallow lattices the expansion is unimodal and ballistic, while strong lattices suppress tunneling. However for intermediate lattice depths a strong interplay between dipolar interaction and lattice depth occurs. The expansion is found to be bimodal, the central cloud expansion can be distinguished from the outer halo structure. In the regime of strongly interactions dipolar bosons exhibit two time scales, with an initial diffusion and then arrested transport in the long time; while strongly interacting bosons in the fermionized limit exhibit ballistic expansion. Our study highlights how different lattice depths and initial states can be manipulated to control tunneling dynamics.

Recent progress in the design and optimization of Neural-Network Quantum States (NQS) have made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a separate NQS from scratch at every point of the phase diagram, we demonstrate that the optimization of a NQS at a highly expressive point of the phase diagram (i.e., close to a phase transition) yields interpretable features that can be reused to accurately describe a wide region across the transition. We demonstrate the feasibility of our approach on different systems in one and two dimensions by initially pretraining a NQS at a given point of the phase diagram, followed by fine-tuning only the output layer for all other points. Notably, the computational cost of the fine-tuning step is very low compared to the pretraining stage. We argue that the reduced cost of this paradigm has significant potential to advance the exploration of condensed matter systems using NQS, mirroring the success of fine-tuning in machine learning and natural language processing.

We investigate the band structure of the three-dimensional Hofstadter model on cubic lattices, with an isotropic magnetic field oriented along the diagonal of the cube with flux $\Phi=2 \pi \cdot m /n$, where $m,n$ are co-prime integers. Using reduced exact diagonalization in momentum space, we show that, at fixed $m$, there exists an integer $n(m)$ associated with a specific value of the magnetic flux, that we denote by $\Phi_c(m) \equiv 2 \pi \cdot m/n(m)$, separating two different regimes. The first one, for fluxes $\Phi<\Phi_c(m)$, is characterized by complete band overlaps, while the second one, for $\Phi>\Phi_c(m)$, features isolated band touching points in the density of states and Weyl points between the $m$- and the $(m+1)$-th bands. In the Hasegawa gauge, the minimum of the $(m+1)$-th band abruptly moves at the critical flux $\Phi_c(m)$ from $k_z=0$ to $k_z=\pi$. We then argue that the limit for large $m$ of $\Phi_c(m)$ exists and it is finite: $\lim_{m\to \infty} \Phi_c(m) \equiv \Phi_c$. Our estimate is $\Phi_c/2\pi=0.1296(1)$. Based on the values of $n(m)$ determined for integers $m\leq60$, we propose a mathematical conjecture for the form of $\Phi_c(m)$ to be used in the large-$m$ limit. The asymptotic critical flux obtained using this conjecture is $\Phi_c^{{\rm (conj)}}/2\pi=7/54$.

The Continuous Spontaneous Localisation (CSL) model is the most studied among collapse models, which describes the breakdown of the superposition principle for macroscopic systems. Here, we derive an upper bound on the parameters of the model by applying it to the rotational noise measured in a recent short-distance gravity experiment [Lee et al., Phys. Rev. Lett. 124, 101101 (2020)]. Specifically, considering the noise affecting the rotational motion, we found that despite being a table-top experiment the bound is only one order of magnitude weaker than that from LIGO for the relevant values of the collapse parameter. Further, we analyse possible ways to optimise the shape of the test mass to enhance the collapse noise by several orders of magnitude and eventually derive stronger bounds that can address the unexplored region of the CSL parameters space.

The study of entanglement in particle physics has been gathering pace in the past few years. It is a new field that is providing important results about the possibility of detecting entanglement and testing Bell inequality at colliders for final states as diverse as top-quark, $\tau$-lepton pairs and $\Lambda$-baryons, massive gauge bosons and vector mesons. In this review, after presenting definitions, tools and basic results that are necessary for understanding these developments, we summarize the main findings -- as published by the beginning of year 2024 -- including analyses of experimental data in $B$ meson decays and top-quark pair production. We include a detailed discussion of the results for both qubit and qutrits systems, that is, final states containing spin one-half and spin one particles. Entanglement has also been proposed as a new tool to constrain new particles and fields beyond the Standard Model and we introduce the reader to this promising feature as well.

We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type $\mathrm{II}_\infty$ von Neumann algebra. We discuss how this algebra can be coupled to the algebra of observable of an infinite reservoir within the canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting dynamics can lead the system towards a nonequilibrium steady state which can be characterized through modular theory. Within this framework we address the definition of entropy production and its relationship to relative entropy, alongside exploring other applications.

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can one then describe the emergence of the classical, well-defined geometry that we observe? Considering that the decoherence-driven quantum-to-classical transition relies on external physical entities, this process cannot account for the emergence of the classical behaviour of the Universe. Here, we show how models of spontaneous collapse of the wavefunction can offer a viable mechanism for explaining such an emergence. We apply it to a simple General Relativity dynamical model for gravity and a perfect fluid. We show that, by starting from a general quantum superposition of different geometries, the collapse dynamics leads to a single geometry, thus providing a possible mechanism for the quantum-to-classical transition of the Universe. Similarly, when applying our dynamics to the physically-equivalent Parametrised Unimodular gravity model, we obtain a collapse on the basis of the cosmological constant, where eventually one precise value is selected, thus providing also a viable explanation for the cosmological constant problem. Our formalism can be easily applied to other quantum cosmological models where we can choose a well-defined clock variable.

Collapse models constitute an alternative to quantum mechanics that solve the well-know quantum measurement problem. In this framework, a novel approach to include dissipation in collapse models has been recently proposed, and awaits experimental validation. Our work establishes experimental bounds on the so-constructed linear-friction dissipative Di\'osi-Penrose (dDP) and Continuous Spontaneous localisation (dCSL) models by exploiting experiments in the field of levitated optomechanics. Our results in the dDP case exclude collapse temperatures below $ 10^{-13}$K and $ 6 \times 10^{-12}$K respectively for values of the localisation length smaller than $10^{-6}$m and $10^{-8}$m. In the dCSL case the entire parameter space is excluded for values of the temperature lower than $6 \times 10^{-9}$K.

We report on an experiment achieving the dynamical generation of non-Gaussian states of motion of a levitated optomechanical system. We access intrinsic Duffing-like non-linearities by squeezing an oscillator's state of motion through rapidly switching the frequency of its trap. We characterize the experimental non-Gaussian state against expectations from simulations and give prospects for the emergence of genuine non-classical features.

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and late-time four-point functions. Explicit computations reveal that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we compute the late-time four-point functions of vector fields at large $N$, demonstrating that their spectral density is meromorphic in the spectral plane and positive along the principal series. These results offer highly nontrivial checks of unitarity and analyticity for cosmological correlators.

We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $\mu$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $\mu=0$ we show that a certain $\mathbb{Z}_2$-valued 't Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any $N$ and any $T>0$. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for $T>0$ of the inhomogeneous chiral phase configuration found at $T=0$ for any $N$ and any $\mu$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $\mu$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings.

We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k\neq 0$. To obtain this result we compute the $\beta$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds.

Anti-de-Sitter space acts as an infra-red cut off for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. We scrutinize the interpolation for theories in two dimensions from the perspective of boundary conformal theories. We show that the appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space. We conjecture a similar mechanism for confinement in gauge theories.

We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d $\mathcal{N}=2$ SCFTs with $\frac{1}{2}$-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial $S^3$. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d $\mathcal{N}=2$ SCFTs on the boundary. In particular we derive the action of the SL(2,$\mathbb{Z}$) duality on the one-point functions.

Quantum magnetism in two-dimensional systems represents a lively branch of modern condensed-matter physics. In the presence of competing super-exchange couplings, magnetic order is frustrated and can be suppressed down to zero temperature, leading to exotic ground states. The Shastry-Sutherland model, describing $S=1/2$ degrees of freedom interacting in a two-dimensional lattice, portrays a simple example of highly-frustrated magnetism, capturing the low-temperature behavior of SrCu$_2$(BO$_3$)$_2$ with its intriguing properties. Here, we investigate this problem by using a Vision Transformer to define an extremely accurate variational wave function. From a technical side, a pivotal achievement relies on using a deep neural network with real-valued parameters, parametrized with a Transformer, to map physical spin configurations into a high-dimensional feature space. Within this abstract space, the determination of the ground-state properties is simplified, requiring only a single output layer with complex-valued parameters. From the physical side, we supply strong evidence for the stabilization of a spin-liquid between the plaquette and antiferromagnetic phases. Our findings underscore the potential of Neural-Network Quantum States as a valuable tool for probing uncharted phases of matter, opening opportunities to establish the properties of many-body systems.

In the last decade, a growing interest has been devoted to models of spontaneous collapse of the wavefunction, known also as collapse models. They coherently solve the well-known quantum measurement problem by suitably modifying the Schr\"odinger evolution. Quantum experiments are now finally within the reach of testing such models (and thus testing the limits of quantum theory). Here, we propose a method based on a two-ions confined in a linear Paul trap to possibly enhance the testing capabilities of such experiments. The combination of an atomic and a macromolecular ion provide a good match for the cooling of the motional degrees of freedom and a non-negligible insight in the collapse mechanism, respectively.

Quantum computers are inherently affected by noise. While in the long-term error correction codes will account for noise at the cost of increasing physical qubits, in the near-term the performance of any quantum algorithm should be tested and simulated in the presence of noise. As noise acts on the hardware, the classical simulation of a quantum algorithm should not be agnostic on the platform used for the computation. In this work, we apply the recently proposed noisy gates approach to efficiently simulate noisy optical circuits described in the dual rail framework. The evolution of the state vector is simulated directly, without requiring the mapping to the density matrix framework. Notably, we test the method on both the gate-based and measurement-based quantum computing models, showing that the approach is very versatile. We also evaluate the performance of a photonic variational quantum algorithm to solve the MAX-2-CUT problem. In particular we design and simulate an ansatz which is resilient to photon losses up to $p \sim 10^{-3}$ making it relevant for near term applications.

We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves two significant advancements. First, we employ a repetition of unitary gates on a set of $n$ system qubits and, remarkably, only a single ancillary bath qubit representing the environment. It follows that, for the typical case of $m$-locality of the Lindblad operators, we reach an exponential improvement of the number of ancilla in terms of $m$ and up to a polynomial improvement in ancilla overhead for large $n$ with respect to other approaches. Although stochasticity is introduced, requiring multiple circuit realizations, the sampling overhead is independent of the system size. Secondly, we show that, under fixed accuracy conditions, our algorithm enables a reduction in the number of trotter steps compared to other approaches, substantially decreasing circuit depth. These advancements hold particular significance for near-term quantum computers, where minimizing both width and depth is critical due to inherent noise in their dynamics.

We investigate the impact of the spin-phonon coupling on the S=1/2 Heisenberg model on the kagome lattice. For the pure spin model, there is increasing evidence that the low-energy properties can be correctly described by a Dirac spin liquid, in which spinons with a conical dispersion are coupled to emergent gauge fields. Within this scenario, the ground-state wave function is well approximated by a Gutzwiller-projected fermionic state [Y. Ran, M. Hermele, P.A. Lee, and X.-G. Wen, Phys. Rev. Lett. 98, 117205 (2007)]. However, the existence of U(1) gauge fields may naturally lead to instabilities when small perturbations are included. Since phonons are ubiquitous in real materials, they may play a relevant role in the determination of the actual physical properties of the kagome antiferromagnet. We perform a step forward in this direction, including phonon degrees of freedom (at the quantum level) and applying a variational approach based upon Gutzwiller-projected fermionic Ans\"atze. Our results suggest that the Dirac spin liquid is stable for small spin-phonon couplings, while valence-bond solids are obtained at large couplings. Even though different distortions can be induced by the spin-phonon interaction, the general aspect is that the energy is lowered by maximizing the density of perfect hexagons in the dimerization pattern.

Arrays of Josephson junctions are at the forefront of research on quantum circuitry for quantum computing, simulation and metrology. They provide a testing bed for exploring a variety of fundamental physical effects where macroscopic phase coherence, nonlinearities and dissipative mechanisms compete. Here we realize finite-circulation states in an atomtronic Josephson junction necklace, consisting of a tunable array of tunneling links in a ring-shaped superfluid. We study the stability diagram of the atomic flow by tuning both the circulation and the number of junctions. We predict theoretically and demonstrate experimentally that the atomic circuit withstands higher circulations (corresponding to higher critical currents) by increasing the number of Josephson links. The increased stability contrasts with the trend of the superfluid fraction -- quantified by Leggett's criterion -- which instead decreases with the number of junctions and the corresponding density depletion. Our results demonstrate atomic superfluids in mesoscopic structured ring potentials as excellent candidates for atomtronics applications, with prospects towards the observation of non-trivial macroscopic superpositions of current states.

n this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question `what are collapse models (and in general any physical theory) about?'; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role.

Optimizing the probability of quantum tunneling between two states, while keeping the resources of the underlying physical system constant, is a task of key importance due to its critical role in various applications. We show that, by applying Machine Learning techniques when the system is coupled to an ancilla, one optimizes the parameters of both the ancillary component and the coupling, ultimately resulting in the maximization of the tunneling probability. We provide illustrative examples for the paradigmatic scenario involving a two-mode system and a two-mode ancilla in the presence of several interacting particles. Physically, the increase of the tunneling probability is rooted in the decrease of the two-well asymmetry due to the coherent oscillations induced by the coupling to the ancilla. We also argue that the enhancement of the tunneling probability is not hampered by weak coupling to noisy environments.

We propose a protocol for the scalable quantum simulation of SU($N$)$\times$U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices in both one- and two-dimensional systems. The protocol exploits the combination of naturally occurring SU($N$) pseudo-spin symmetry and strong inter-orbital interactions that is unique to such atomic species. A detailed ab initio study of the microscopic dynamics shows how gauge invariance emerges in an accessible parameter regime, and allows us to identify the main challenges in the simulation of such theories. We provide quantitative results about the requirements in terms of experimental stability in relation to observing gauge invariant dynamics, a key element for a deeper analysis on the functioning of such class of theories in both quantum simulators and computers.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle.

Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as entanglement and superposition of states. Among the known quantum algorithms, a special role is played by the Shor algorithm, i.e. a polynomial-time quantum algorithm for integer factorization, with far reaching potential applications in several fields, such as cryptography. Here we present a different algorithm for integer factorization based on another genuine quantum property: quantum measurement. In this new scheme, the factorization of the integer $N$ is achieved in a number of steps equal to the number $k$ of its prime factors, -- e.g., if $N$ is the product of two primes, two quantum measurements are enough, regardless of the number of digits $n$ of the number $N$. Since $k$ is the lower bound to the number of operations one can do to factorize a general integer, one sees that a quantum mechanical setup can saturate such a bound.

Given the key role that quantum tunneling plays in a wide range of applications, a crucial objective is to maximize the probability of tunneling from one quantum state/level to another, while keeping the resources of the underlying physical system fixed. In this work, we demonstrate that an effective solution to this challenge can be achieved by coupling the tunneling system with an ancillary system of the same kind. By utilizing machine learning techniques, the parameters of both the ancillary system and the coupling can be optimized, leading to the maximization of the tunneling probability. We provide illustrative examples for the paradigmatic scenario involving a two-mode system and a two-mode ancilla with arbitrary couplings and in the presence of several interacting particles. Importantly, the enhancement of the tunneling probability appears to be minimally affected by noise and decoherence in both the system and the ancilla.

The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the $U(1)$ Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyse the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor super-exchange couplings, and the Dirac state corresponds to the lowest-energy Ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.

Quantum secure direct communication (QSDC) is a rapidly developing quantum communication approach, where secure information is directly transmitted, providing an alternative to key-based (de)encryption processes via Quantum Key Distribution (QKD). During the last decade, optical QSDC protocols based on discrete variable encodings have been successfully realized. Recently, continuous-variable (CV) QSDC schemes have been proposed, benefiting from less-sophisticated implementations with proven security. Here, we report the first table-top experimental demonstration of a CV-QSDC system and assess its security. For this realization, we analyze the security of different configurations, including coherent and squeezed sources, with Wyner wiretap channel theory in presence of a beam splitter attack. This practical protocol not only demonstrates the principle of QSDC systems based on CV encoding, but also showcases the advantage of squeezed states over coherent ones in attaining enhanced security and reliable communication in lossy and noisy channels. Our realization, which is founded on mature telecom components, paves the way into future threat-less quantum metropolitan networks, compatible with coexisting advanced wavelength division multiplexing (WDM) systems.

We investigate the role of vortices in the decay of persistent current states of annular atomic superfluids by solving numerically the Gross-Pitaevskii equation, and we directly compare our results with experimental data from Ref. [1]. We theoretically model the optical phase-imprinting technique employed to experimentally excite finite-circulation states in Ref. [1] in the Bose-Einstein condensation regime, accounting for imperfections of the optical gradient imprinting profile. By comparing simulations of this realistic protocol to an ideal imprinting, we show that the introduced density excitations arising from imperfect imprinting are mainly responsible for limiting the maximum reachable winding number $w_\mathrm{max}$ in the superfluid ring. We also investigate the effect of a point-like obstacle with variable potential height $V_0$ onto the decay of circulating supercurrents. For a given obstacle height, a critical circulation $w_c$ exists, such that for an initial circulation $w_0$ larger than $w_c$ the supercurrent decays through the emission of vortices, which cross the superflow and thus induce phase slippage. Higher values of the obstacle height $V_0$ further favour the entrance of vortices, thus leading to lower values of $w_c$. Furthermore, the stronger vortex-defect interaction at higher $V_0$ leads to vortices that propagate closer to the center of the ring condensate. The combination of both these effects leads to an increase of the supercurrent decay rate for increasing $w_0$, in agreement with experimental observations. [1]: G. Del Pace, et al., Phys. Rev. X 12, 041037 (2022)

K\'arolyh\'azy's original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated K\'arolyh\'azy's assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal.

We consider scalar QED with $N_f$ flavors in AdS$_D$. For $D<4$ the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large $N_f$. We then apply this result to compute the boundary four-point function of the charged operators at leading order in $1/N_f$ and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large $N_f$, in integer dimension $D= 3$ an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.

Critical behaviour in phase transitions is a resource for enhanced precision metrology. The reason is that the function, known as Fisher information, is superextensive at critical points, and, at the same time, quantifies performances of metrological protocols. Therefore, preparing metrological probes at phase transitions provides enhanced precision in measuring the transition control parameter. We focus on the Lipkin-Meshkov-Glick model that exhibits excited state quantum phase transitions at different magnetic fields. Resting on the model spectral properties, we show broad peaks of the Fisher information, and propose efficient schemes for precision magnetometry. The Lipkin-Meshkov-Glick model was first introduced for superconductivity and for nuclear systems, and recently realised in several condensed matter platforms. The above metrological schemes can be also exploited to measure microscopic properties of systems able to simulate the Lipkin-Meshkov-Glick model.

Geometric Semantic Geometric Programming (GSGP) is one of the most prominent Genetic Programming (GP) variants, thanks to its solid theoretical background, the excellent performance achieved, and the execution time significantly smaller than standard syntax-based GP. In recent years, a new mutation operator, Geometric Semantic Mutation with Local Search (GSM-LS), has been proposed to include a local search step in the mutation process based on the idea that performing a linear regression during the mutation can allow for a faster convergence to good-quality solutions. While GSM-LS helps the convergence of the evolutionary search, it is prone to overfitting. Thus, it was suggested to use GSM-LS only for a limited number of generations and, subsequently, to switch back to standard geometric semantic mutation. A more recently defined variant of GSGP (called GSGP-reg) also includes a local search step but shares similar strengths and weaknesses with GSM-LS. Here we explore multiple possibilities to limit the overfitting of GSM-LS and GSGP-reg, ranging from adaptive methods to estimate the risk of overfitting at each mutation to a simple regularized regression. The results show that the method used to limit overfitting is not that important: providing that a technique to control overfitting is used, it is possible to consistently outperform standard GSGP on both training and unseen data. The obtained results allow practitioners to better understand the role of local search in GSGP and demonstrate that simple regularization strategies are effective in controlling overfitting.

Despite their impressive performance in classification tasks, neural networks are known to be vulnerable to adversarial attacks, subtle perturbations of the input data designed to deceive the model. In this work, we investigate the relation between these perturbations and the implicit bias of neural networks trained with gradient-based algorithms. To this end, we analyse the network's implicit bias through the lens of the Fourier transform. Specifically, we identify the minimal and most critical frequencies necessary for accurate classification or misclassification respectively for each input image and its adversarially perturbed version, and uncover the correlation among those. To this end, among other methods, we use a newly introduced technique capable of detecting non-linear correlations between high-dimensional datasets. Our results provide empirical evidence that the network bias in Fourier space and the target frequencies of adversarial attacks are highly correlated and suggest new potential strategies for adversarial defence.

We show that a two-body Jastrow wave function is able to capture the ground-state properties of the $S=1$ antiferromagnetic Heisenberg chain with the single-ion anisotropy term, in both the topological and trivial phases. Here, the optimized Jastrow pseudo potential assumes a very simple form in Fourier space, i.e., $v_{q} \approx 1/q^2$, which is able to give rise to a finite string-order parameter in the topological regime. The results are analysed by using an exact mapping from the quantum expectation values over the variational state to the classical partition function of the one-dimensional Coulomb gas of particles with charge $q=\pm 1$. Here, two phases are present at low temperatures: the first one is a diluted gas of dipoles (bound states of particles with opposite charges), which are randomly oriented (describing the trivial phase); the other one is a dense liquid of dipoles, which are aligned thanks to the residual dipole-dipole interactions (describing the topological phase, with the finite string order being related to the dipole alignment). Our results provide an insightful interpretation of the ground-state nature of the spin-1 antiferromagnetic Heisenberg model.

A two-dimensional layer of oxide reveals itself as a essential element to drive the photocatalytic activity in a nanostructured hybrid material, which combines high-quality epitaxial graphene and titanium dioxide nanoparticles. In particular, it has been revealed that the addition of a 2D Ti oxide layer sandwiched between graphene and metal induces a p-doping of graphene and a consistent shift in the Ti d states. These modifications induced by the interfacial oxide layer induce a reduction of the probability of charge carrier recombination and enhance the photocatalytic activity of the heterostructure. This is indicative of a capital role played by thin oxide films in fine-tuning the properties of heterostructures based on graphene and pave the way to new combinations of graphene/oxides for photocatalysis-oriented applications.

We discuss the generation and the long-time persistence of entanglement in open two-qubit systems whose reduced dissipative dynamics is not apriori engineered but is instead subjected to filtering and Markovian feedback. In particular, we analytically study 1.) whether the latter operations may enhance the environment capability of generating entanglement at short times and 2.) whether the generated entaglement survives in the long-time regime. We show that, in the case of particularly symmetric Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) it is possible to fully control the convex set of stationary states of the two-qubit reduced dynamics, therefore the asymptotic behaviour of any initial two-qubit state. We then study the impact of a suitable class of feed-back operations on the considered dynamics.

We argue that, in the quest for the translation of fundamental research into actual quantum technologies, two avenues that have - so far - only partly explored should be pursued vigorously. On first entails that the study of energetics at the fundamental quantum level holds the promises for the design of a generation of more energy-efficient quantum devices. On second route to pursue implies a more structural hybridisation of quantum dynamics with data science techniques and tools, for a more powerful framework for quantum information processing.

We perform a numerical study of transport properties of a one-dimensional chain with couplings decaying as an inverse power $r^{-(1+\sigma)}$ of the intersite distance $r$ and open boundary conditions, interacting with two heat reservoirs. Despite its simplicity, the model displays highly nontrivial features in the strong long-range regime, $-1<\sigma<0$. At weak coupling with the reservoirs, the energy flux departs from the predictions of perturbative theory and displays anomalous superdiffusive scaling of the heat current with the chain size. We trace back this behavior to the transmission spectrum of the chain, which displays a self-similar structure with a characteristic sigma-dependent fractal dimension.

Although different architectures of quantum perceptrons have been recently put forward, the capabilities of such quantum devices versus their classical counterparts remain debated. Here, we consider random patterns and targets independently distributed with biased probabilities and investigate the storage capacity of a continuous quantum perceptron model that admits a classical limit, thus facilitating the comparison of performances. Such a more general context extends a previous study of the quantum storage capacity where using statistical mechanics techniques in the limit of a large number of inputs, it was proved that no quantum advantages are to be expected concerning the storage properties. This outcome is due to the fuzziness inevitably introduced by the intrinsic stochasticity of quantum devices. We strengthen such an indication by showing that the possibility of indefinitely enhancing the storage capacity for highly correlated patterns, as it occurs in a classical setting, is instead prevented at the quantum level.

The electronic properties of graphene can be modified by the local interaction with a selected metal substrate. To probe this effect, Scanning Tunneling Microscopy is widely employed, particularly by means of local measurement via lock-in amplifier of the differential conductance and of the field emission resonance. In this article we propose an alternative, reliable method of probing the graphene/substrate interaction that is readily available to any STM apparatus. By testing the tunneling current as function of the tip/sample distance on nanostructured graphene on Ni(100), we demonstrate that I(z) spectroscopy can be quantitatively compared with Density Functional Theory calculations and can be used to assess the nature of the interaction between graphene and substrate. This method can expand the capabilities of standard STM systems to study graphene/substrate complexes, complementing standard topographic probing with spectroscopic information.

K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface string theory associates an Elliptic genus, a certain partition function directly related to the theory of Jacobi modular forms. A multiplicative lift of the Elliptic genus produces another modular object, an Igusa cusp form, which is the generating function of BPS invariants of K3 x E. In this note we will discuss a refinement of this chain of ideas. The Elliptic genus can be generalized to the so called Hodge-Elliptic genus which is then related to the counting of refined BPS states of K3 x E. We show how such BPS invariants can be computed explicitly in terms of different versions of the Hodge-Elliptic genus, sometimes in closed form, and discuss some generalizations.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the assumption of a Gaussian dynamics. We consider two different problems: 1) the dynamics of a levitated nanoparticle undergoing the transition from an harmonic to a double-well potential; 2) the transfer of a quantum state across a double-well potential through classical and quantum protocols. In both cases, we assume that the system undergoes to decoherence and thermalisation. In case 1), we construct a numerical approach to the problem and study the non-equilibrium thermodynamics of the system. In case 2), we introduce a new figure of merit to quantify the efficiency of a state-transfer protocol and apply it to quantum and classical versions of such protocols.

Collapse models describe the breakdown of the quantum superposition principle when moving from microscopic to macroscopic scales. They are among the possible solutions to the quantum measurement problem and thus describe the emergence of classical mechanics from the quantum one. Testing collapse models is equivalent to test the limits of quantum mechanics. I will provide an overview on how one can test collapse models, and which are the future theoretical and experimental challenges ahead.

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

We study the effects of the electromagnetic vacuum on the motion of a nonrelativistic electron. First, we derive the equation of motion for the expectation value of the electron's position operator. We show how this equation has the same form as the classical Abraham-Lorentz equation but, at the same time, is free of the well known runaway solution. Second, we study decoherence induced by vacuum fluctuations. We show that decoherence due to vacuum fluctuations that appears at the level of the reduced density matrix of the electron, obtained after tracing over the radiation field, does not correspond to actual irreversible loss of coherence.

In this work the spontaneous electromagnetic radiation from atomic systems, induced by dynamical wave-function collapse, is investigated in the X-rays domain. Strong departures are evidenced with respect to the simple cases considered until now in the literature, in which the emission is either perfectly coherent (protons in the same nuclei) or incoherent (electrons). In this low-energy regime the spontaneous radiation rate strongly depends on the atomic species under investigation and, for the first time, is found to depend on the specific collapse model.

We construct and study the simplest universal dissipative Lindblad master equation for many-body systems with the purpose of a new dissipative extension of existing nonrelativistic theories of fundamental spontaneous decoherence and spontaneous wave function collapse in nature. It is universal as it is written in terms of second-quantized mass density $\hat \rho$ and current $\hat J$, thus making it independent of the material structure and its parameters. Assuming linear friction in the current, we find that the dissipative structure is strictly constrained. Following the general structure of our dissipative Lindblad equation, we derive and analyze the dissipative extensions of the two most known spontaneous wave function collapse models, the Di\'osi-Penrose and the continuous spontaneous localization models.

We consider three-dimensional Quantum Electrodynamics in the presence of a Chern-Simons term at level $k$ and $N_f$ flavors, in the limit of large $N_f$ and $k$ with $k/N_f$ fixed. We consider either bosonic or fermionic matter fields, with and without quartic terms at criticality: the resulting theories are critical and tricritical bosonic QED$_3$, Gross-Neveu and fermionic QED$_3$. For all such theories we compute the effective potentials and the $\beta$ functions of classically marginal couplings, at the leading order in the large $N_f$ limit and to all orders in $k/N_f$ and in the couplings. We determine the RG fixed points and discuss the quantum stability of the corresponding vacua. While critical bosonic and fermionic QED$_3$ are always stable CFTs, we find that tricritical bosonic and Gross-Neveu QED$_3$ exist as stable CFTs only for specific values of $k/N_f$. Finally, we discuss the phase diagrams of these theories as a function of their relevant deformations.

We present a novel method for simulating the noisy behaviour of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM Qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behaviour of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at this link: https://pypi.org/project/quantum-gates.

We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $\epsilon$-expansion around $d=4$. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in $d>4$ or $d<4$. In the first case we extrapolate to $d=5$ to test a recently proposed construction of the UV fixed point of $5d$ $SU(2)$ Yang-Mills via a susy-breaking deformation of the $E_1$ SCFT. We find that the $F$ theorem allows the proposed RG flow. In the second case we extrapolate to $d=3$ to test whether QCD$_3$ with gauge group $SU(n_c)$ and $n_f$ fundamental matter fields flows to a CFT or to a symmetry-breaking phase. We find that within the regime with a real gauge coupling near $d=4$ the CFT phase is always favored. For lower values of $n_f$ we compare the average of $F$ between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value $n_f^*$ below which the symmetry-breaking phase takes over.

Manipulating quantum systems undergoing non-Gaussian dynamics in a fast and accurate manner is becoming fundamental to many quantum applications. Here, we focus on classical and quantum protocols transferring a state across a double-well potential. The classical protocols are achieved by deforming the potential, while the quantum ones are assisted by a counter-diabatic driving. We show that quantum protocols perform more quickly and accurately. Finally, we design a figure of merit for the performance of the transfer protocols -- namely, the \textit{protocol grading} -- that depends only on fundamental physical quantities, and which accounts for the quantum speed limit, the fidelity and the thermodynamic of the process. We test the protocol grading with classical and quantum protocols, and show that quantum protocols have higher protocol grading than the classical ones.

We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behaviour of LN is discussed in the B - D plane, including a separating line - ending in a triple point - where the energy density is independent on the size. Finally, results for LN at finite temperature as a function of B and D are presented and commented.

An M-class mission proposal in response to the 2021 call in ESA's science programme with a broad range of objectives in fundamental physics, which include testing the Equivalence Principle and Lorentz Invariance, searching for Ultralight Dark Matter and probing Quantum Mechanics.

The Transformer architecture has become the state-of-art model for natural language processing tasks and, more recently, also for computer vision tasks, thus defining the Vision Transformer (ViT) architecture. The key feature is the ability to describe long-range correlations among the elements of the input sequences, through the so-called self-attention mechanism. Here, we propose an adaptation of the ViT architecture with complex parameters to define a new class of variational neural-network states for quantum many-body systems, the ViT wave function. We apply this idea to the one-dimensional $J_1$-$J_2$ Heisenberg model, demonstrating that a relatively simple parametrization gets excellent results for both gapped and gapless phases. In this case, excellent accuracies are obtained by a relatively shallow architecture, with a single layer of self-attention, thus largely simplifying the original architecture. Still, the optimization of a deeper structure is possible and can be used for more challenging models, most notably highly-frustrated systems in two dimensions. The success of the ViT wave function relies on mixing both local and global operations, thus enabling the study of large systems with high accuracy.

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a non-perturbative one tied to angular momentum conservation, and a perturbative one. A comparison with other schemes for $(2+1)$-dimensional quantum link models present in literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent $\alpha$. We add to the Hamiltonian an anisotropy in the $z$-direction. In the framework of a semiclassical approach, we use the Holstein-Primakoff transformation to derive an effective long-range discrete nonlinear Schr\"odinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schr\"odinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for $\alpha < 3$. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent $\alpha$.

Convolutional neural networks (CNNs) have been employed along with Variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. In order to do so, however, a CNN with only linearly many variational parameters has to circumvent the ``curse of dimensionality'' and successfully approximate a wavefunction on an exponentially large Hilbert space. In our work, we provide a theoretical and experimental analysis of how the CNN optimizes learning for spin systems, and investigate the CNN's low dimensional approximation. We first quantify the role played by physical symmetries of the underlying spin system during training. We incorporate our insights into a new training algorithm and demonstrate its improved efficiency, accuracy and robustness. We then further investigate the CNN's ability to approximate wavefunctions by looking at the entanglement spectrum captured by the size of the convolutional filter. Our insights reveal the CNN to be an ansatz fundamentally centered around the occurrence statistics of $K$-motifs of the input strings. We use this motivation to provide the shallow CNN ansatz with a unifying theoretical interpretation in terms of other well-known statistical and physical ansatzes such as the maximum entropy (MaxEnt) and entangled plaquette correlator product states (EP-CPS). Using regression analysis, we find further relationships between the CNN's approximations of the different motifs' expectation values. Our results allow us to gain a comprehensive, improved understanding of how CNNs successfully approximate quantum spin Hamiltonians and to use that understanding to improve CNN performance.

The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor $XY$ model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional $XY$ model has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, $\sigma$, in which there are a magnetized, a disordered and a critical phase (arXiv:2104.13217). Here we address the issue of whether the critical behavior of the two-dimensional $XY$ model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range $XY$ model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for $\sigma<2$ the two models no longer share the same universality class. Remarkably, within a large region of its phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with $1/r^2$ interactions.

Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on the fact that, according to these models, the dynamics is driven by a noise that, besides collapsing the wave function in space, generates a diffusive motion with characteristic signatures, which, though small, can be tested. The non-interferometric approach might seem applicable only to those models which implement the collapse through a noisy dynamics, not to any model, which collapses the wave function in space. Here we show that this is not the case: under reasonable assumptions, any collapse dynamics (in space) is diffusive. Specifically, we prove that any space-translation invariant dynamics which complies with the no-signaling constraint, if collapsing the wave function in space, must change the average momentum of the system, and/or its spread.

"Strange" correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and non-translational invariant cases, and in presence of on-site disorder and long-range couplings, extend the validity of the strange correlators approach for the diagnosis of topological phases of matter, and indicate a general procedure for their optimal choice.

The measurement of quantum entanglement can provide a new and most sensitive probe to physics beyond the Standard Model. We use the concurrence of the top-quark pair spin states produced at colliders to constrain the magnetic dipole term in the coupling between top quark and gluons, that of $\tau$-lepton pairs spin states to bound contact interactions and that of $\tau$-lepton pairs or two-photons spin states from the decay of the Higgs boson in trying to distinguish between CP-even and odd couplings. These four examples show the power of the new approach as well as its limitations. We show that differences in the entanglement in the top-quark and $\tau$-lepton pair production cross sections can provide constraints better than those previously estimated from total cross sections or classical correlations. Instead, the final states in the decays of the Higgs boson remain maximally entangled even in the presence of CP odd couplings and cannot be used to set bounds on new physics. We discuss the violation of Bell inequalities featured in all four processes.

Conversion of chemical energy into mechanical work is the fundamental mechanism of several natural phenomena at the nanoscale, like molecular machines and Brownian motors. Quantum mechanical effects are relevant for optimising these processes and to implement them at the atomic scale. This paper focuses on engines that transform chemical work into mechanical work through energy and particle exchanges with thermal sources at different chemical potentials. Irreversibility is introduced by modelling the engine transformations with finite-time dynamics generated by a time-depending quantum master equation. Quantum degenerate gases provide maximum efficiency for reversible engines, whereas the classical limit implies small efficiency. For irreversible engines, both the output power and the efficiency at maximum power are much larger in the quantum regime than in the classical limit. The analysis of ideal homogeneous gases grasps the impact of quantum statistics on the above performances, which persists in the presence of interactions and more general trapping. The performance dependence on different types of Bose-Einstein Condensates (BECs) is also studied. BECs under considerations are standard BECs with a finite fraction of particles in the ground state, and generalised BECs where eigenstates with parallel momenta, or those with coplanar momenta are macroscopically occupied according to the confinement anisotropy. Quantum statistics is therefore a resource for enhanced performances of converting chemical into mechanical work.

Motivated by recent experiments on Cs$_2$Cu$_3$SnF$_{12}$ and YCu$_{3}$(OH)$_{6}$Cl$_{3}$, we consider the ${S=1/2}$ Heisenberg model on the kagome lattice with nearest-neighbor super-exchange $J$ and (out-of-plane) Dzyaloshinskii-Moriya interaction $J_D$, which favors (in-plane) ${\bf Q}=(0,0)$ magnetic order. By using both variational Monte Carlo (based upon Gutzwiller-projected fermionic wave functions) and tensor-network approaches (built from infinite projected-entangled pair/simplex states), we show that the ground state develops a finite magnetization for $J_D/J \gtrsim 0.03 - 0.04$, while the gapless spin liquid remains stable for smaller values of the Dzyaloshinskii-Moriya interaction. The relatively small value of $J_D/J$ for which magnetic order sets in is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$. In addition, we assess the spin dynamical structure factors and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is reported within the magnetically ordered phase, similarly to what has been detected by inelastic neutron scattering on Cs$_{2}$Cu$_{3}$SnF$_{12}$.

Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the {\it Ansatz} by the optimization of its building blocks, i.e., tensors characterized by bond dimension $D$, and the extrapolation scheme to reach the "thermodynamic" limit $D \to \infty$. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture the spontaneous breaking of a continuous symmetry in phases such as the antiferromagnetic (N\'eel) phase with high fidelity, in addition to valence-bond solids which are already well described by finite-$D$ iPEPS. In contrast, systems in the vicinity of continuous quantum phase transitions still present a challenge for iPEPS, especially when non-abelian symmetries are involved. Here, we consider the iPEPS Ansatz to describe the continuous transition between the (gapless) antiferromagnet and the (gapped) paramagnet that exists in the $S=1/2$ Heisenberg model on coupled two-leg ladders. In particular, we show how accurate iPEPS results can be obtained down to a narrow interval around criticality and analyze the scaling of the order parameter in the N\'eel phase in a spatially anisotropic situation.

Many scenarios beyond the standard model, aiming to solve long-standing cosmological and particle physics problems, suggest that dark matter might experience long-distance interactions mediated by an unbroken dark $U(1)$ gauge symmetry, hence foreseeing the existence of a massless dark photon. Contrary to the massive dark photon, a massless dark photon can only couple to the standard model sector by means of effective higher dimensional operators. Massless dark-photon production at colliders will then in general be suppressed at low energy by a UV energy scale, which is of the order of the masses of portal (messenger) fields connecting the dark and the observable sectors. A violation of this expectation is provided by dark-photon production mediated by the Higgs boson, thanks to the non-decoupling Higgs properties. Higgs-boson production at colliders, followed by the Higgs decay into a photon and a dark photon, provides then a very promising production mechanism for the dark photon discovery, being insensitive in particular regimes to the UV scale of the new physics. This decay channel gives rise to a peculiar signature characterized by a monochromatic photon with energy half the Higgs mass (in the Higgs rest frame) plus missing energy. We show how such resonant photon-plus-missing-energy signature can uniquely be connected to a dark photon production. Higgs boson production and decay into a photon and a dark photon as a source of dark photons is reviewed at the Large Hadron Collider, in the light of the present bounds on the corresponding signature by the CMS and ATLAS collaborations. Perspectives for the dark-photon production in Higgs-mediated processes at future $e^+e^-$ colliders are also discussed.

Computational methods are driving high impact microscopy techniques such as ptychography. However, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close-to-the-hardware programming constructs to speed up the reconstruction. In this paper, we present SciComPty, a new ptychography software framework aiming at simulating ptychography datasets and testing state-of-the-art and new reconstruction algorithms. Despite its simplicity, the software leverages GPU accelerated processing through the PyTorch CUDA interface. This is essential to design new methods that can readily be employed. As an example, we present an improved position refinement method based on Adam and a new version of the rPIE algorithm, adapted for partial coherence setups. Results are shown on both synthetic and real datasets. The software is released as open-source.

We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous and discrete symmetry groups, as well as more refined details such as the charges of the hypermultiplets under these groups. We derive these data by means of a gauge-theoretic method, that we have recently introduced, based on establishing a correspondence between an adjoint Higgs field and the M-theory geometry. As a byproduct, this further allows us to construct several T-brane backgrounds, that yield inequivalent 5d spectra but are associated with the same geometry.

The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds from holomorphic reflection involutions of such hypersurfaces with Hodge numbers $h^{1,1}\leq 12$. In particular, we compute orientifold configurations for all favourable FRSTs for $h^{1,1}\leq 7$, while randomly sampling triangulations for each pair of Hodge numbers up to $h^{1,1}=12$. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from O$p$-planes grows linearly with the number of complex structure and K\"ahler moduli. We further consider non-local D7-tadpole cancellation through Whitney branes. We argue that this leads to a significant enhancement of the total D3-tadpole as compared to conventional $\mathrm{SO}(8)$ stacks with $(4+4)$ D7-branes on top of O7-planes. In particular, before turning-on worldvolume fluxes, we find that the largest D3-tadpole in this class occurs for Calabi-Yau threefolds with $(h^{1,1}_{+},h^{1,2}_{-})=(11,491)$ with D3-brane charges $|Q_{\text{D3}}|=504$ for the local D7 case and $|Q_{\text{D3}}|=6,664$ for the non-local Whitney branes case, which appears to be large enough to cancel tadpoles and allow fluxes to stabilise all complex structure moduli. Our data is publicly available under http://github.com/AndreasSchachner/CY_Orientifold_database .