Electrical transport in the Hatsugai-Kohmoto model
Guerci D., Sangiovanni G., Millis A.J., 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.
Nonstabilizerness in U(1) lattice gauge theory
Falcão P.R.N., Tarabunga P.S., Frau M., Tirrito E., Zakrzewski J., 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.
Many-body localization in the age of classical computing
Sierant P., Lewenstein M., 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.
Ensemble inequivalence in Ising chains with competing interactions
Campa A., Hovhannisyan V., Ruffo S., 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.
Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function
Piccioni D., Ferrari F., 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.
Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems
Lerose A., Parolini T., Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special nonequilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work, we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent α of spin-spin interactions from the solvable permutationally symmetric limit α=0. First, we numerically establish that, despite the fact that spectral signatures of chaos appear for infinitesimal α, the towers of α=0 energy eigenstates with large collective spin are smoothly deformed as α is increased and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor nonlinearly coupled to an extensive set of bosonic modes. We analytically solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation and show their self-consistent localization in large-spin sectors of the original Hamiltonian for 0<α
Nonequilibrium Dynamics of Charged Dual-Unitary Circuits
Foligno A., 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.
Cluster property and Bell inequalities
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.
Energy exchange statistics and fluctuation theorem for nonthermal asymptotic states
Hernández-Gómez S., Poggiali F., Cappellaro P., Cataliotti F.S., Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik 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 nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition I for the existence of an energy scale factor η∗ that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This η∗ plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition 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 I is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.
Retrieving nonstabilizerness with neural networks
Mello A.F., Lami G., 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.
One-dimensional quench dynamics in an optical lattice: Sine-Gordon and Bose-Hubbard descriptions
Roy S., Roy R., 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.
Altermagnetism from interaction-driven itinerant magnetism
Giuli S., Mejuto-Zaera C., 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.