Entanglement asymmetry as a probe of symmetry breaking

Ares F., Murciano S., Symmetry and symmetry breaking are two pillars of modern quantum physics. Still, quantifying how much a symmetry is broken is an issue that has received little attention. In extended quantum systems, this problem is intrinsically bound to the subsystem of interest. Hence, in this work, we borrow methods from the theory of entanglement in many-body quantum systems to introduce a subsystem measure of symmetry breaking that we dub entanglement asymmetry. As a prototypical illustration, we study the entanglement asymmetry in a quantum quench of a spin chain in which an initially broken global U(1) symmetry is restored dynamically. We adapt the quasiparticle picture for entanglement evolution to the analytic determination of the entanglement asymmetry. We find, expectedly, that larger is the subsystem, slower is the restoration, but also the counterintuitive result that more the symmetry is initially broken, faster it is restored, a sort of quantum Mpemba effect, a phenomenon that we show to occur in a large variety of systems.

Entanglement generation through Markovian feed-back in open two-qubit systems

We discuss the generation and the long-time persistence of entanglement in open two-qubit systems whose reduced dissipative dynamics is not a priori 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 entanglement survives in the long-time regime. We show that, in the case of particularly symmetric Gorini-Kossakowski-Sudarshan-Lindblad 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.

TREXIO: A file format and library for quantum chemistry

Posenitskiy E., Chilkuri V.G., Ammar A., Hapka M., Pernal K., Shinde R., Landinez Borda E.J., Filippi C., Nakano K., Kohulák O., TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the hierarchical data format version 5 library, which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for Fortran, Python, and OCaml programming languages. In addition, a suite of tools have been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

Quantum multicritical behavior for coupled optical cavities with driven laser fields

Hu Y., Zhou Y., Luo W., Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.

Toward Chemical Accuracy Using the Jastrow Correlated Antisymmetrized Geminal Power Ansatz

Raghav A., Maezono R., Hongo K., Herein, we report accurate atomization energy calculations for 55 molecules in the Gaussian-2 (G2) set using lattice regularized diffusion Monte Carlo (LRDMC). We compare the Jastrow-Slater determinant ansatz with a more flexible JsAGPs (Jastrow correlated antisymmetrized geminal power with singlet correlation) ansatz. AGPs is built from pairing functions, which explicitly include pairwise correlations among electrons, and hence, this ansatz is expected to be more efficient in recovering the correlation energy. The AGPs wave functions are first optimized at the variational Monte Carlo (VMC) level, which includes both the Jastrow factor and the nodal surface optimization. This is followed by the LRDMC projection of the ansatz. Remarkably, for many molecules, the LRDMC atomization energies obtained using the JsAGPs ansatz reach chemical accuracy (∼1 kcal/mol), and for most other molecules, the atomization energies are accurate within ∼5 kcal/mol. We obtained a mean absolute deviation of 1.6 kcal/mol with JsAGPs and 3.2 kcal/mol with JDFT (Jastrow factor + Slater determinant with DFT orbitals) ansatzes. This work shows the effectiveness of the flexible AGPs ansatz for atomization energy calculations and electronic structure simulations in general.

Coherent control of the orbital occupation driving the insulator-to-metal Mott transition in V2 O3

Franceschini P., Policht V.R., Milloch A., Ronchi A., Mor S., Mellaerts S., Hsu W.F., Pagliara S., Ferrini G., Banfi F., Managing light-matter interactions on timescales faster than the loss of electronic coherence is key for achieving full quantum control of the final products in solid-solid transformations. In this Letter, we demonstrate coherent optical control of the orbital occupation that determines the insulator-to-metal transition in the prototypical Mott insulator V2O3. Selective excitation of a specific interband transition with two phase-locked light pulses manipulates the occupation of the correlated bands in a way that depends on the coherent evolution of the photoinduced superposition of states. A comparison between experimental results and numerical solutions of the optical Bloch equations provides an electronic coherence time on the order of 5 fs. Temperature-dependent experiments suggest that the electronic coherence time is enhanced in the vicinity of the insulator-to-metal transition critical temperature, thus highlighting the role of fluctuations in determining the electronic coherence. These results open different routes to selectively switch the functionalities of quantum materials and coherently control solid-solid electronic transformations.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge - inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state - seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

Stochastic representation of the quantum quartic oscillator

Tucci G., De Nicola S., Wald S., Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.

Collapse Models: A Theoretical, Experimental and Philosophical Review

In 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.

Entanglement of stationary states in the presence of unstable quasiparticles

Horváth D.X., The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.

Quantum simulator of link models using spinor dipolar ultracold atoms

Fontana P., Barros J.C.P., 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 nonperturbative one tied to angular-momentum conservation, and a perturbative one. A comparison with other schemes for (2+1)-dimensional quantum link models present in the literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

Probing the Degree of Coherence through the Full 1D to 3D Crossover

Shah R., Barrett T.J., Colcelli A., Oručević F., We experimentally study a gas of quantum degenerate Rb87 atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential μ controls the departure of the system from 3D and that the fluctuations are dependent on both μ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.

Stability of many-body localization in Floquet systems

Sierant P., Lewenstein M., We study many-body localization (MBL) transition in disordered Floquet systems using a polynomially filtered exact diagonalization (POLFED) algorithm. We focus on disordered kicked Ising model and quantitatively demonstrate that finite-size effects at the MBL transition are less severe than in the random field XXZ spin chains widely studied in the context of MBL. Our conclusions extend also to other disordered Floquet models, indicating smaller finite-size effects than those observed in the usually considered disordered autonomous spin chains. We observe consistent signatures of the transition to MBL phase for several indicators of ergodicity breaking in the kicked Ising model. Moreover, we show that an assumption of a power-law divergence of the correlation length at the MBL transition yields a critical exponent ν≈2, consistent with the Harris criterion for one-dimensional disordered systems.

Systematically improvable mean-field variational ansatz for strongly correlated systems: Application to the Hubbard model

A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature Teff is defined, probing the distance of the ground-state properties of the model in the thermodynamic limit from the ones of the proposed correlated mean-field ansatz. In this way, their uncertainties from the unbiased zero temperature limit may be estimated by simple and stable extrapolations well before the so-called sign problem gets prohibitive. At finite Teff, the convergence of the energy to the thermodynamic limit is indeed shown to already be possible in the Hubbard model for relatively small square lattices with linear dimension L≃10, thanks to appropriate averages over several twisted boundary conditions. Within the estimated energy accuracy of the proposed variational ansatz, two clear phases are identified, as the energy is lowered by spontaneously breaking some symmetries satisfied by the Hubbard Hamiltonian: (a) a stripe phase where both spin and translation symmetries are broken and (b) a strong coupling d-wave superconducting phase when the particle number is not conserved and global U(1) symmetry is broken. On the other hand, the symmetric phase is stable in a wide region at large doping and small coupling.

Exciton condensation in strongly correlated quantum spin Hall insulators

Amaricci A., Mazza G., Capone M., Time-reversal symmetric topological insulators are generically robust with respect to weak local interaction unless symmetry-breaking transitions take place. Using dynamical mean-field theory, we solve an interacting model of quantum spin Hall insulators and show the existence at intermediate coupling of a symmetry-breaking transition to a nontopological insulator characterized by exciton condensation. This transition is of first order. For a larger interaction strength, the insulator evolves into a Mott one. The transition is continuous if magnetic order is prevented, and notably, for any finite Hund's exchange, it progresses through a Mott localization before the condensate coherence is lost. We show that the correlated excitonic state corresponds to a magneto-electric insulator, which allows for direct experimental probing. Finally, we discuss the fate of the helical edge modes across the excitonic transition.

Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement

Arias R., Di Giulio G., Keski-Vakkuri E., We compare the capacity of entanglement with the entanglement entropy by considering various aspects of these quantities for free bosonic and fermionic models in one spatial dimension, both in the continuum and on the lattice. Substantial differences are observed in the subleading terms of these entanglement quantifiers when the subsystem is made by two disjoint intervals, in the massive scalar field and in the fermionic chain. We define c-functions based on the capacity of entanglement similar to the one based on the entanglement entropy, showing through a numerical analysis that they display a monotonic behaviour under the renormalisation group flow generated by the mass. The capacity of entanglement and its related quantities are employed to explore the symmetry resolution. The temporal evolutions of the capacity of entanglement and of the corresponding contour function after a global quench are also discussed.

Wetting critical behavior in the quantum Ising model within the framework of Lindblad dissipative dynamics

Artiaco C., Nava A., We investigate the critical behavior, both in space and time, of the wetting interface within the coexistence region around the first-order phase transition of a fully connected quantum Ising model in slab geometry. For that, we employ the Lindblad master equation formalism in which temperature is inherited by the coupling to a dissipative bath, rather than being a functional parameter as in the conventional Cahn's free energy. Lindblad's approach gives not only access to the dissipative dynamics and steady-state configuration of the quantum wetting interface throughout the whole phase diagram but also shows that the wetting critical behavior can be successfully exploited to characterize the phase diagram as an alternative to the direct evaluation of the free energies of the competing phases.

Entanglement resolution of free Dirac fermions on a torus

Foligno A., Murciano S., Whenever a system possesses a conserved charge, the density matrix splits into eigenspaces associated to the each symmetry sector and we can access the entanglement entropy in a given subspace, known as symmetry resolved entanglement (SRE). Here, we first evaluate the SRE for massless Dirac fermions in a system at finite temperature and size, i.e. on a torus. Then we add a massive term to the Dirac action and we treat it as a perturbation of the massless theory. The charge-dependent entropies turn out to be equally distributed among all the symmetry sectors at leading order. However, we find subleading corrections which depend both on the mass and on the boundary conditions along the torus. We also study the resolution of the fermionic negativity in terms of the charge imbalance between two subsystems. We show that also for this quantity, the presence of the mass alters the equipartition among the different imbalance sectors at subleading order.

Villain model with long-range couplings

Giachetti G., Defenu N., Ruffo S., 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 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, σ, in which there are a magnetized, a disordered and a critical phase [1]. 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 σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.

Erratum: Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles (Phys. Rev. B (2022) 105 (L241114) DOI: 10.1103/PhysRevB.107.L241114)

Turkeshi X., Our paper introduced a phenomenological quasiparticle picture describing monitored many-body systems. A central point of our work is that the system's non-Hermitian Hamiltonian (nHH) quasiparticles reveal insights into the measurement-induced phases. In particular, the quasiparticle picture explains the emergence of a logarithmic phase in noninteracting monitored fermions when the nHH gap is closed and an area-law phase when the nHH gap is open [a fact numerically observed in a variety of works (see, e.g., Ref. [1])] To qualitatively support our claims, we have introduced an archetypal model: the transverse field Ising chain under quantum jumps monitoring of the transverse magnetization. Here, the correlation matrix fully captures the dynamics by the system's Gaussianity. (Figure Presented). In conclusion, the new analysis confirms the qualitative description given by the quasiparticle picture for monitored fermionic systems in a wide range of parameters, provided finite-size effects are considered. We are grateful to A. Paviglianiti and A. Silva for pointing out a problem in our original numerical implementation.