arXiv subjects

Vincenzo Alba

Publications and source records attributed to Vincenzo Alba.

At least 37 records · Page 2Linked to original sources

arXiv2023

Entanglement gap in 1D long-range quantum spherical models

We investigate the finite-size scaling of the entanglement gap in the one dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent $α$. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The entanglement gap decays as $δξ\simeq C_αL^{-(1/2-α/4)}$, where the constant $C_α$ depends on the low-energy properties of the model. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.

cond-mat.stat-mech↗

arXiv2023

Symmetry-resolved entanglement in fermionic systems with dissipation

We investigate symmetry-resolved entanglement in out-of-equilibrium fermionic systems subject to gain and loss dissipation, which preserves the block-diagonal structure of the reduced density matrix. We derive a hydrodynamic description of the dynamics of several entanglement-related quantities, such as the symmetry-resolved von Neumann entropy and the charge-imbalance-resolved fermionic negativity. We show that all these quantities admit a hydrodynamic description in terms of entangled quasiparticles. While the entropy is dominated by dissipative processes, the resolved negativity is sensitive to the presence of entangled quasiparticles, and it shows the typical ``rise and fall'' dynamics. Our results hold in the weak-dissipative hydrodynamic limit of large intervals, long times and weak dissipation rates.

cond-mat.stat-mech↗

arXiv2023

Entanglement negativity in a fermionic chain with dissipative defects: Exact results

We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the Rényi mutual information with Rényi index $1/2$, in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.

cond-mat.stat-mech↗

arXiv2023

Entanglement in the Quantum Spherical Model -- a Review

We review some recent results on entanglement in the Quantum Spherical Model (QSM). The focus lays on the physical results rather than the mathematical details. Specifically, we study several entanglement-related quantities, such asentanglement entropies, and logarithmic negativity, in the presence of quantum and classical critical points, and in magnetically ordered phases. We consider both the short as well as the long-range QSM. The study of entanglement properties of the QSM is feasible because the model is mappable to a Gaussian system in any dimension. Despite this fact the QSM is an ideal theoretical laboratory to investigate a wide variety of physical scenarios, such as non mean field criticality, the effect of long-range interactions, the interplay between finite-temperature fluctuations and genuine quantum ones.

cond-mat.stat-mech↗

arXiv2022

Dissipative quasi-particle picture for quadratic Markovian open quantum systems

Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic theories or tensor networks, can accurately capture the time-evolution of subsystem entropies, thus allowing for a profound understanding of the unitary dynamics of quantum correlations. However, so far, these methods either cannot be applied to open quantum systems or do not permit an efficient computation of quantum entropies for mixed states. Here, we make progress in solving this issue by formulating a dissipative quasi-particle picture -- describing the dynamics of quantum entropies in the hydrodynamic limit -- for a general class of noninteracting open quantum systems. Our results show that also in dissipative many-body systems, correlations are generically established through the propagation of quasi-particles.

cond-mat.stat-mech↗

arXiv2022

Logarithmic entanglement scaling in dissipative free-fermion systems

We study the quantum information spreading in one-dimensional free-fermion systems in the presence of localized thermal baths. We employ a nonlocal Lindblad master equation to describe the system-bath interaction, in the sense that the Lindblad operators are written in terms of the Bogoliubov operators of the closed system, and hence are nonlocal in space. The statistical ensemble describing the steady state is written in terms of a convex combination of the Fermi-Dirac distributions of the baths. Due to the singularity of the free-fermion dispersion, the steady-state mutual information exhibits singularities as a function of the system parameters. While the mutual information generically satisfies an area law, at the singular points it exhibits logarithmic scaling as a function of subsystem size. By employing the Fisher-Hartwig theorem, we derive the prefactor of the logarithmic scaling, which depends on the parameters of the baths and plays the role of an effective "central charge". This is upper bounded by the central charge governing ground-state entanglement scaling. We provide numerical checks of our results in the paradigmatic tight-binding chain and the Kitaev chain.

cond-mat.stat-mech↗

arXiv2022

Entangled multiplets and unusual spreading of quantum correlations in a continuously monitored tight-binding chain

We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and continuous monitoring. We unveil the existence of multipartite quantum correlations which are inconsistent with an entangled-pair structure and which, within a quasiparticle picture, would require the presence of larger multiplets. We also observe that quantum information is highly delocalized, as it is shared in a collective {\it nonredundant} way among adjacent regions of the many-body system. Our results shed new light onto the behavior of correlations in quantum stochastic dynamics and further show that these may be enhanced by a (weak) continuous monitoring process.

cond-mat.stat-mech↗

arXiv2022

Rise and fall, and slow rise again, of operator entanglement under dephasing

The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a $U(1)$ conservation law. We argue that in an XXZ spin-model and a Bose-Hubbard model the OE grows universally as $\frac{1}{4} \log_2 t$ at long times, and as $\frac{1}{2} \log_2 t$ for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.

quant-ph↗

arXiv2022

Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture

Rényi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out-of-equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterisation is a key objective of current research. Here we show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.

cond-mat.stat-mech↗

arXiv2022

Hydrodynamics of quantum entropies in Ising chains with linear dissipation

We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities -- such as the von Neumann entropy, the Rényi entropies, and the associated mutual information -- admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.

cond-mat.stat-mech↗

arXiv2022

Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. We focus on the hydrodynamic limit of large distances from the source of dissipation and of long times, with their ratio being fixed. In this limit, the localized dissipation gives rise to an effective delta potential (dissipative impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of dissipation for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong dissipation the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.

cond-mat.stat-mech↗

arXiv2021

Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

cond-mat.stat-mech↗

arXiv2021

Quench dynamics of Rényi negativities and the quasiparticle picture

The study of the moments of the partially transposed density matrix provides a new and effective way of detecting bipartite entanglement in a many-body mixed state. This is valuable for cold-atom and ion-trap experiments, as well as in the general context of quantum simulation of many-body systems. In this work we study the time evolution after a quantum quench of the moments of the partial transpose, and several related quantities, such as the Rényi negativities. By combining Conformal Field Theory (CFT) results with integrability, we show that, in the space-time scaling limit of long times and large subsystems, a quasiparticle description allows for a complete understanding of the Rényi negativities. We test our analytical predictions against exact numerical results for free-fermion and free-boson lattice models, even though our framework applies to generic interacting integrable systems.

cond-mat.stat-mech↗

arXiv2021

Diffusion and operator entanglement spreading

Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles. We derive the logarithmic bound $1/2\ln(t)$ for the $OSEE$ of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg $XXZ$ chain. Away from the isotropic point and from the free-fermion point, the $OSEE$ grows as $1/2\ln(t)$, irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent from probing the asymptotic behavior of the $OSEE$.

cond-mat.stat-mech↗

arXiv2021

Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems

We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.

cond-mat.str-el↗

arXiv2021

Unbounded entanglement production via a dissipative impurity

We investigate the entanglement dynamics in a free-fermion chain initially prepared in a Fermi sea and subjected to localized losses (dissipative impurity). We derive a formula describing the dynamics of the entanglement entropies in the hydrodynamic limit of long times and large intervals. The result depends only on the absorption coefficient of the effective delta potential describing the impurity in the hydrodynamic limit. Genuine dissipation-induced entanglement is certified by the linear growth of the logarithmic negativity. Finally, in the quantum Zeno regime at strong dissipation the entanglement growth is arrested (Zeno entanglement death).

cond-mat.stat-mech↗

arXiv2020

Entanglement gap, corners, and symmetry breaking

We investigate the finite-size scaling of the lowest entanglement gap $δξ$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $δξ=Ω/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $δξ=π^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $Ω$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $Ω$, at least for the case of a square corner.

cond-mat.stat-mech↗

arXiv2020

Closure of the entanglement gap at quantum criticality: The case of the Quantum Spherical Model

The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap $δξ$, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition, and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as $π^2/\ln(L)$, with $L$ the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap $δξ\ln(L)$ exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a non-trivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.

cond-mat.stat-mech↗