Publications

We employ the quasiparticle picture of entanglement evolution to obtain an effective description for the out-of-equilibrium entanglement Hamiltonian at the hydrodynamical scale following quantum quenches in free fermionic systems in two or more spatial dimensions. Specifically, we begin by applying dimensional reduction techniques in cases where the geometry permits, building directly on established results from one-dimensional systems. Subsequently, we generalize the analysis to encompass a wider range of geometries. We obtain analytical expressions for the entanglement Hamiltonian valid at the ballistic scale, which reproduce the known quasiparticle picture predictions for the Renyi entropies and full counting statistics. We also numerically validate the results with excellent precision by considering quantum quenches from several initial configurations.

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory.

The behavior of the helicity modulus has been frequently employed to investigate the onset of the topological order characterizing the low-temperature phase of the two-dimensional XY model. We here present how the analysis based on the use of this key quantity can be applied to the study of the properties of coupled layers. To this aim, we first discuss how to extend the popular worm algorithm to a layered sample, and in particular to the evaluation of the longitudinal helicity, that we introduce taking care of the fact that the virtual twist representing the elastic deformation one applies to properly define the helicity modulus can act on a single layer or on all of them. We then apply the method to investigate the bilayer XY model, showing how the helicity modulus can be used to determine the phase diagram of the model as a function of temperature and interlayer coupling strength.

Odd-diffusive systems, characterised by broken time-reversal and/or parity, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we extend the investigation to the high-density limit of an odd tracer embedded in a soft medium described by the Gaussian core model (GCM) using a field-theoretic approach based on the Dean-Kawasaki equation. Our analysis reveals that interactions can enhance the dynamics of an odd tracer even in dense systems. We demonstrate that oddness results in a complete reversal of the well-known self-diffusion ( D s ) anomaly of the GCM. Ordinarily, D s exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, D0, ( D s < D 0 ) so that D s ↑ D 0 at high densities. In contrast, for an odd tracer, self-diffusion is enhanced ( D s > D 0 ) and the GCM anomaly is inverted, displaying D s ↓ D 0 at high densities. The transition between the standard and reversed GCM anomaly is governed by the tracer’s oddness, with a critical oddness value at which the tracer diffuses as a free particle ( D s ≈ D 0 ) across all densities. We validate our theoretical predictions with Brownian dynamics simulations, finding strong agreement between the them.

We investigate the use of a boundary time crystals (BTCs) as quantum sensors of AC fields. Boundary time crystals are non-equilibrium phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time translation symmetry. We find an enhanced sensitivity of the BTC when its spins are resonant with the applied AC field, as quantified by the quantum Fisher information (QFI). The QFI dynamics in this regime is shown to be captured by a relatively simple Ansatz consisting of an initial power-law growth and late-time exponential decay. We study the scaling of the Ansatz parameters with resources (encoding time and number of spins) and identify a moderate quantum enhancement in the sensor performance through comparison with classical QFI bounds. Investigating the precise source of this performance, we find that despite of its long coherence time and multipartite correlations (advantageous properties for quantum metrology), the entropic cost of the BTC (which grows indefinitely in the thermodynamic limit) hinders an optimal decoding of the AC field information. This result has implications for future candidates of quantum sensors in open system and we hope it will encourage future study into the role of entropy in quantum metrology.

We introduce a general approximate method for calculating the one-body correlations and the momentum distributions of one-dimensional Bose gases at finite interaction strengths and temperatures trapped in smooth confining potentials. Our method combines asymptotic techniques for the long-distance behavior of the gas (similar to Luttinger liquid theory) with known short-distance expansions. We derive analytical results for the limiting cases of strong and weak interactions and provide a general procedure for calculating one-body correlations at any interaction strength. A step-by-step explanation of the numerical method used to compute Green's functions (needed as input to our theory) is included. We benchmark our method against exact numerical calculations and compare its predictions to recent experimental results.

We show that in models with the Hatsugai-Kohmoto type of interaction that is local in momentum space thus infinite range in real space, Kubo formulas neither reproduce the correct thermodynamic susceptibilities, nor yield sensible transport coefficients. Using Kohn's trick to differentiate between metals and insulators by threading a flux in a torus geometry, we uncover the striking property that Hatsugai-Kohmoto models with an interaction-induced gap in the spectrum sustain a current that grows as the linear size at any nonzero flux and which can be either diamagnetic or paramagnetic.

We present a thorough investigation of nonstabilizerness - a fundamental quantum resource that quantifies state complexity within the framework of quantum computing - in a one-dimensional U(1) lattice gauge theory including matter fields. We show how nonstabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that nonstabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (which, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations.

The optimal "twisted"geometry of a crystalline layer on a crystal has long been known, but that on a quasicrystal is still unknown and open. We predict analytically that the layer equilibrium configuration will generally exhibit a nonzero misfit angle. The theory perfectly agrees with numerical optimization of a colloid monolayer on a quasiperiodic decagonal optical lattice. Strikingly different from crystal-on-crystal epitaxy, the structure of the novel emerging twisted state exhibits an unexpected stripe pattern. Its high anisotropy should reflect on the tribomechanical properties of this unconventional interface.

Nonadiabatic effects in the electron-phonon coupling are important whenever the ratio between the phononic and the electronic energy scales - the adiabatic ratio - is non-negligible. For superconducting systems, this gives rise to additional diagrams in the superconducting self-energy, the vertex, and cross-corrections. In this work, we explore these corrections in a two-dimensional single-band system through the crossover between the weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein regimes. By focusing on the pseudogap phase, we identify the parameter range in which the pairing amplitude is amplified by nonadiabatic effects and, due to controlled approximations, we map them throughout the BCS-BEC crossover. These effects become stronger as the system is driven deeply in the crossover regime, for phonon frequencies of the order of the hopping energy and for large enough electron-phonon coupling. Finally, we provide the phase space regions in which the effects of nonadiabaticity are more relevant for unconventional superconductors.

Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase, in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.

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 nearest-neighbor (NN) and next-NN 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.

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 the 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). In the latter case, instead, a finite spin gap remains at small 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.

Among the many loopholes that might be invoked to reconcile local realism with the experimental violations of Bell inequalities, the space dependence of the correlation functions appears particularly relevant for its connections with the so-called cluster property, one of the basic ingredients of axiomatic quantum field theory. The property states that the expectation values of products of observables supported within spacelike separated space-time regions factorize. Actually, in some massive models the factorization is exponentially fast with respect to the distance between the systems possibly involved in actual experiments. It is then often argued that considering the space dependence of the quantities involved in the Bell-like inequalities would eventually not violate them and thus support the reproducibility of the quantum behavior by a suitable local hidden variable model. In this paper, we show when this is actually the case and how nonlocal effects can still be visible.

The interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the center of an intense multidisciplinary research effort. Here we introduce a setting where these questions can be characterized exactly by considering dual-unitary circuits with an arbitrary number of U(1) charges. After providing a complete characterization of these systems we show that one can introduce a class of solvable states, which extends that of generic dual-unitary circuits, for which the nonequilibrium dynamics can be solved exactly. In contrast to the known class of solvable states, which relax to the infinite-temperature state, these states relax to a family of nontrivial generalized Gibbs ensembles. The relaxation process of these states can be simply described by a linear growth of the entanglement entropy followed by saturation to a nonmaximal value but with maximal entanglement velocity. We then move on to consider the dynamics from nonsolvable states, combining the exact results with the entanglement membrane picture we argue that the entanglement dynamics from these states is qualitatively different from that of the solvable ones. It shows two different growth regimes characterized by two distinct slopes, both corresponding to submaximal entanglement velocities. Moreover, we show that nonsolvable initial states can give rise to the quantum Mpemba effect, where less symmetric initial states restore the symmetry faster than more symmetric ones.

Altermagnetism, a new phase of collinear spin-order sharing similarities with antiferromagnets and ferromagnets, has introduced a new guiding principle for spintronic and thermoelectric applications because of its direction-dependent magnetic properties. Fulfilling the promise to exploit altermagnetism for device design depends on identifying materials with tuneable transport properties. The search for intrinsic altermagnets has so far focused on the role of anisotropy in the crystallographic symmetries and in the band structure. Here, we present a different mechanism that approaches this goal by leveraging the interplay between a Hubbard local repulsion and the itinerant magnetism given by the presence of van Hove singularities. We show that altermagnetism is stable for a broad range of interactions and dopings and we focus on tunability of the spin-charge conversion ratio.

Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a different approach leveraging convolutional neural networks (CNNs) to classify quantum states based on their nonstabilizerness content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between stabilizer Rényi entropies and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources.

We investigate the dynamical deconfinement transition driven by excitations in a long-range Ising model. At low temperatures, spatially separated pairs of domain wall kinks are bound by the confining potential and exhibit uncorrelated Bloch oscillations in time. This picture is analogous to bound mesons in quark confinement. As the temperature increases, the meson picture breaks down as the domain wall kinks in proximity interact and disperse, leading to an extended deconfined regime. In this paper, we characterize the deconfinement transition with signatures observed in the average density of domain wall kinks and nonequilibrium changes in its fluctuation. Our findings provide insights into the mechanisms of confinement and deconfinement in long-range spin models, thus opening avenues for further exploration and experimental verification.

We study the explicit breaking of a SU(2) symmetry to a U(1) subgroup employing the entanglement asymmetry, a recently introduced observable that measures how much symmetries are broken in a part of extended quantum systems. We consider as specific model the critical XXZ spin chain, which breaks the SU(2) symmetry of spin rotations except at the isotropic point, and is described by the massless compact boson in the continuum limit. We examine the U(1) subgroup of SU(2) that is broken outside the isotropic point by applying conformal perturbation theory, which we complement with numerical simulations on the lattice. We also analyse the entanglement asymmetry of the full SU(2) group. By relying on very generic scaling arguments, we derive an asymptotic expression for it.

We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the weakly interacting (Bose-Hubbard) and strongly interacting (sine-Gordon) regimes. While in a higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in one dimension 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 sine-Gordon model. The present work aims at identifying the quench dynamics in both the Bose-Hubbard and sine-Gordon interaction regimes. We numerically exactly solve the time-dependent Schrödinger equation for a small number of atoms and obtain dynamical measures of several key quantities. We investigate the correlation dynamics of first and second order; both exhibit rich many-body features in the dynamics. We conclude that in both cases, dynamics exhibits collapse-revival phenomena, though with different timescales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics especially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. Bose-Hubbard dynamics clearly establishes the possible relaxation to the maximum entropy state. In contrast, the sine-Gordon dynamics is so fast that it does not exhibit any signature of relaxation in the present timescale of computation.