arXiv subjects

Vincenzo Alba

Publications and source records attributed to Vincenzo Alba.

At least 55 records · Page 3Linked to original sources

arXiv2020

Entanglement revivals as a probe of scrambling in finite quantum systems

The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.

cond-mat.stat-mech↗

arXiv2020

Entanglement equipartition in critical random spin chains

The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement entropy for one dimensional conformal and integrable systems. In this paper, we extend this equipartition theorem to the disordered critical systems by studying the random singlet phase. We analytically compute the disorder averaged symmetry resolved Rényi entropies and show the leading orders are independent of the symmetry sector. Our findings are cross-checked with simulations within the numerical strong disorder renormalization group. We also identify the first subleading term breaking equipartition which is of the form $s^2/\ln\ell$ where $s$ is the magnetization of a subsystem of length $\ell$.

cond-mat.stat-mech↗

arXiv2020

Spreading of correlations in Markovian open quantum systems

Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For {\it isolated} systems, a hydrodynamic theory explains the origin and spreading of entanglement via the propagation of quasi-particle pairs. However, when systems interact with their surrounding much less has been established. Here we show that the quasi-particle picture remains valid for open quantum systems: while information is still spread by quasiparticles, the environment modifies their correlation and introduces incoherent and mixing effects. For free fermions with gain/loss dissipation we provide formulae fully describing incoherent and quasiparticle contributions in the spreading of entropy and mutual information. Importantly, the latter is not affected by incoherent correlations. The mutual information is exponentially damped at short times and eventually vanishes signalling the onset of a classical limit. The behaviour of the logarithmic negativity is similar and this scenario is common to other dissipations. For weak dissipation, the presence of quasiparticles underlies remarkable scaling behaviors.

cond-mat.stat-mech↗

arXiv2020

Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics

We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply the flea gas simulation of GHD to obtain numerical results for entanglement growth. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ spin chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. While the flea gas method applied to the XXZ chain is not exact even in the scaling limit (in contrast to the Lieb--Liniger model), it yields a very good approximation of analytical results for entanglement growth in the cases considered. Furthermore, we obtain the {\it full-time} dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

cond-mat.stat-mech↗

arXiv2019

Entanglement and classical fluctuations at finite-temperature critical points

We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature $T$ and of the quantum parameter $g$, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any $g$ and $T$, the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of $g,T$, the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any $g$, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough $T$. The vanishing of the negativity defines a "death line", which we characterise analytically at small $g$. Importantly, for any finite $T$ the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit $T\to 0$. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

cond-mat.stat-mech↗

arXiv2019

Quantum information scrambling after a quantum quench

How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two intervals of fixed length as a function of their distance is a diagnostic tool for scrambling after a quantum quench. We consider both integrable and non-integrable one dimensional systems. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading, predicting, in the scaling limit of large intervals and times, a decay exponent equal to $1/2$. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers.

cond-mat.stat-mech↗

arXiv2019

Generalized hydrodynamics with space-time inhomogeneous interactions

We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally-motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical Sinh-Gordon model.

cond-mat.stat-mech↗

arXiv2019

Quantum information dynamics in multipartite integrable systems

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index $α=1/2$. We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.

cond-mat.stat-mech↗

arXiv2019

Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain

In a many-body quantum system, local operators in Heisenberg picture $O(t) = e^{i H t} O e^{-i H t}$ spread as time increases. Recent studies have attempted to find features of that spreading which could distinguish between chaotic and integrable dynamics. The operator entanglement - the entanglement entropy in operator space - is a natural candidate to provide such a distinction. Indeed, while it is believed that the operator entanglement grows linearly with time $t$ in chaotic systems, numerics suggests that it grows only logarithmically in integrable systems. That logarithmic growth has already been established for non-interacting fermions, however progress on interacting integrable systems has proved very difficult. Here, for the first time, a logarithmic upper bound is established rigorously for all local operators in such a system: the `Rule 54' qubit chain, a model of cellular automaton introduced in the 1990s [Bobenko et al., CMP 158, 127 (1993)], recently advertised as the simplest representative of interacting integrable systems. Physically, the logarithmic bound originates from the fact that the dynamics of the models is mapped onto the one of stable quasiparticles that scatter elastically; the possibility of generalizing this scenario to other interacting integrable systems is briefly discussed.

cond-mat.stat-mech↗

arXiv2019

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.

cond-mat.stat-mech↗

arXiv2019

Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems

We investigate the steady-state Rényi entanglement entropies after a quench from a piecewise homogeneous initial state in integrable models. In the quench protocol two macroscopically different chains (leads) are joined together at the initial time, and the subsequent dynamics is studied. We study the entropies of a finite subsystem at the interface between the two leads. The density of Rényi entropies coincides with that of the entropies of the Generalized Gibbs Ensemble (GGE) that describes the interface between the chains. By combining the Generalized Hydrodynamics (GHD) treatment of the quench with the Bethe ansatz approach for the Rényi entropies, we provide exact results for quenches from several initial states in the anisotropic Heisenberg chain (XXZ chain), although the approach is applicable, in principle, to any low-entangled initial state and any integrable model. An interesting protocol that we consider is the expansion quench, in which one of the two leads is prepared in the vacuum of the model excitations. An intriguing feature is that for moderately large anisotropy the transport of bound-state is not allowed. Moreover, we show that there is a `critical' anisotropy, above which bound-state transport is permitted. This is reflected in the steady-state entropies, which for large enough anisotropy do not contain information about the bound states. Finally, we benchmark our results against time-dependent Density Matrix Renormalization Group (tDMRG) simulations.

cond-mat.stat-mech↗

arXiv2018

Rényi entropies after releasing the Néel state in the XXZ spin-chain

We study the Rényi entropies in the spin-$1/2$ anisotropic Heisenberg chain after a quantum quench starting from the Néel state. The quench action method allows us to obtain the stationary Rényi entropies for arbitrary values of the index $α$ as generalised free energies evaluated over a calculable thermodynamic macrostate depending on $α$. We work out this macrostate for several values of $α$ and of the anisotropy $Δ$ by solving the thermodynamic Bethe ansatz equations. By varying $α$ different regions of the Hamiltonian spectrum are accessed. The two extremes are $α\to\infty$ for which the thermodynamic macrostate is either the ground state or a low-lying excited state (depending on $Δ$) and $α=0$ when the macrostate is the infinite temperature state. The Rényi entropies are easily obtained from the macrostate as function of $α$ and a few interesting limits are analytically characterised. We provide robust numerical evidence to confirm our results using exact diagonalisation and a stochastic numerical implementation of Bethe ansatz. Finally, using tDMRG we calculate the time evolution of the Rényi entanglement entropies. For large subsystems and for any $α$, their density turns out to be compatible with that of the thermodynamic Rényi entropies

cond-mat.stat-mech↗

arXiv2018

Rényi entropies of generic thermodynamic macrostates in integrable systems

We study the behaviour of Rényi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the Rényi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary Rényi entropies after the quench from the dimer and the tilted Néel state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full details the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies.

cond-mat.stat-mech↗

arXiv2018

Unusual area-law violation in random inhomogeneous systems

The discovery of novel entanglement patterns in quantum many-body systems is a prominent research direction in contemporary physics. Here we provide the example of a spin chain with random and inhomogeneous couplings that in the ground state exhibits a very unusual area law violation. In the clean limit, i.e., without disorder, the model is the rainbow chain and has volume law entanglement. We show that, in the presence of disorder, the entanglement entropy exhibits a power-law growth with the subsystem size, with an exponent 1/2. By employing the Strong Disorder Renormalization Group (SDRG) framework, we show that this exponent is related to the survival probability of certain random walks. The ground state of the model exhibits extended regions of short-range singlets (that we term ``bubble'' regions) as well as rare long range singlet (``rainbow'' regions). Crucially, while the probability of extended rainbow regions decays exponentially with their size, that of the bubble regions is power law. We provide strong numerical evidence for the correctness of SDRG results by exploiting the free-fermion solution of the model. Finally, we investigate the role of interactions by considering the random inhomogeneous XXZ spin chain. Within the SDRG framework and in the strong inhomogeneous limit, we show that the above area-law violation takes place only at the free-fermion point of phase diagram. This point divides two extended regions, which exhibit volume-law and area-law entanglement, respectively.

cond-mat.str-el↗

arXiv2018

Entanglement and quantum transport in integrable systems

Understanding the entanglement structure of out-of-equilibrium many-body systems is a challenging yet revealing task. Here we investigate the entanglement dynamics after a quench from a piecewise homogeneous initial state in integrable systems. This is the prototypical setup for studying quantum transport, and it consists in the sudden junction of two macroscopically different and homogeneous states. By exploiting the recently developed integrable hydrodynamic approach and the quasiparticle picture for the entanglement dynamics, we conjecture a formula for the entanglement production rate after joining two semi-infinite reservoirs, as well as the steady-state entanglement entropy of a finite subregion. We show that both quantities are determined by the quasiparticles created in the Non Equilibrium steady State (NESS) appearing at large times at the interface between the two reservoirs. Specifically, the steady-state entropy coincides with the thermodynamic entropy of the NESS, whereas the entropy production rate reflects its spreading into the bulk of the two reservoirs. Our results are numerically corroborated using time-dependent Density Matrix Renormalization Group (tDMRG) simulations in the paradigmatic XXZ spin-1/2 chain.

cond-mat.stat-mech↗

arXiv2018

Entanglement dynamics after quantum quenches in generic integrable systems

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

cond-mat.stat-mech↗

arXiv2017

Quench action and Renyi entropies in integrable systems

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalisation to Renyi entropies. We develop a new technique to calculate the diagonal Renyi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Renyi entropies are generalised free energies evaluated over a thermodynamic macrostate which depends on the Renyi index and, in particular, it is not the same describing the von Neumann entropy. The technical reason for this, maybe surprising, result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Renyi entropies encode information about different regions of the spectrum of the post-quench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalise this result to the case of arbitrary Renyi entropy.

cond-mat.stat-mech↗

arXiv2017

Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories

We investigate the effect of a global degeneracy in the distribution of entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the non-integer degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spin-chains provides strong analytical evidences corroborating our results.

hep-th↗