Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

Abstract

We consider the non-equilibrium dynamics of the entanglement entropy of a onedimensional quantum gas of hard-core particles, initially confined in a box potential at zero temperature. At t = 0 the right edge of the box is suddenly released and the system is let free to expand. During this expansion, the initially correlated region propagates with a non-homogeneous profile, leading to the growth of entanglement entropy. This setting is investigated in the hydrodynamic regime, with tools stemming from semi-classical Wigner function approach and with recent developments of quantum fluctuating hydrodynamics. Within this framework, the entanglement entropy can be associated to a correlation function of chiral twist-fields of the conformal field theory that lives along the Fermi contour and it can be exactly determined. Our predictions for the entanglement evolution are found in agreement with and generalize previous results in literature based on numerical calculations and heuristic arguments.

Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy

“…This allows us to introduce the main notations and concepts, in particular the concept of multiple (or split) Fermi seas, and of the Fermi contour in phase space. There, we also clarify the main difference between this work and previous works [5,34].…”

“…We stress that the appearance of multiple Fermi seas is a major difference with respect to the situations addressed in references [5,34]. While there the hydrodynamic problem is equivalent to a conventional form of hydrodynamics, the protocol considered here (as well as in reference [19]) is the simplest generalization where GHD is really needed (see also reference [4]).…”

Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics

“…While we have focused on one particular protocol, more general settings can be analyzed using the same approach, including non-zero magnetic fields, trapping potentials or geometric quenches [79]. As a follow up, it would also important to quantify the effect of quantum fluctuations on top of the GHD solution, adapting recent approaches for Bose gases and spin-chains [80][81][82][83][84]. Overall, our work shows how GHD is capable of predicting SCS effects in interacting multicomponent quantum gases in versatile experimentally-relevant situations.…”

Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy

“…This allows us to introduce the main notations and concepts, in particular the concept of multiple (or split) Fermi seas, and of the Fermi contour in phase space. There, we also clarify the main difference between this work and previous works [5,34]. In Section III we present our results for the correlations of density fluctuations, and in Section IV the results for the entanglement entropy.…”

“…We stress that the appearance of multiple Fermi seas is a major difference w.r.t the situations addressed in Refs. [5,34]. While there the hydrodynamic problem is equivalent to a conventional form of hydrodynamics, the protocol considered here (as well as in Ref.…”