Entanglement dynamics of a hard-core quantum gas during a Joule expansion

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially confined in a box of size $L$ with saturated density $\rho=1$. The gas is suddenly released into a region of size $2L$ by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum fluctuating hydrodynamics holds quantitatively true even after several reflections of the gas against the box edges. We further investigate the long time limit $t/L\gg 1$ where a Floquet picture of the non-equilibrium dynamics emerges and hydrodynamics eventually breaks down.Comment: 24 pages, 15 figure

Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: a dimensional reduction treatment

We study the time evolution of the R\'enyi entanglement entropies following a quantum quench in a two-dimensional (2D) free-fermion system. By employing dimensional reduction, we effectively transform the 2D problem into decoupled chains, a technique applicable when the system exhibits translational invariance in one direction. Various initial configurations are examined, revealing that the behavior of entanglement entropies can often be explained by adapting the one-dimensional quasiparticle picture. However, intriguingly, for specific initial states the entanglement entropy saturates to a finite value without the reduced density matrix converging to a stationary state. We discuss the conditions necessary for a stationary state to exist and delve into the necessary modifications to the quasiparticle picture when such a state is absent.Comment: 24 pages, 11 figure

Entanglement of several blocks in fermionic chains

In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and conjecture a formula for the asymptotic behavior of principal submatrices of a Toeplitz matrix

Entanglement asymmetry as a probe of symmetry breaking

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.Comment: 7 pages, 5 figures. Text reorganized, new results for interacting integrable and non-integrable spin chains added. Final version published in Nature Communication

Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study

We consider the quantum quench in the XX spin chain starting from a tilted N\'eel state which explicitly breaks the $U(1)$ symmetry of the post-quench Hamiltonian. Very surprisingly, the $U(1)$ symmetry is not restored at large time because of the activation of a non-abelian set of charges which all break it. The breaking of the symmetry can be effectively and quantitatively characterised by the recently introduced entanglement asymmetry. By a combination of exact calculations and quasi-particle picture arguments, we are able to exactly describe the behaviour of the asymmetry at any time after the quench. Furthermore we show that the stationary behaviour is completely captured by a non-abelian generalised Gibbs ensemble. While our computations have been performed for a non-interacting spin chain, we expect similar results to hold for the integrable interacting case as well because of the presence of non-abelian charges also in that case.Comment: 25 pages, 5 figures. Typos corrected, references adde

Sublogarithmic behaviour of the entanglement entropy in fermionic chains

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szeg\H{o} Theorem or the Fisher-Hartwig conjecture.Comment: 30 pages, 4 figures, 1 table. Final version to appear in JSTAT. One new figure. Some comments and references adde

Complex behavior of the density in composite quantum systems

In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the pattern of this distribution. We discuss the main features of the latter and explain analytically those that we understand. In particular, we prove that it is a nonperturbative property and we find out a large/small coupling constant duality. We also find and study features that may connect our problem with certain aspects of nonlinear classical dynamics, such as the existence of resonances and sensitive dependence on the state of the system. We show that the latter has, indeed, a similar origin than in classical mechanics: the appearance of small denominators in the perturbative series. Inspired by the proof of the Kolmogorov-Arnold-Moser theorem, we are able to deal with this problem by introducing a cutoff in energies that eliminates these small denominators. We also formulate some conjectures that we are not able to prove at present but can be supported by numerical experiments