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 one-dimensional 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.

Entanglement Hamiltonian during a domain wall melting in the free Fermi chain

“…To our best knowledge, a similar result is only known for the dynamics of a driven Tonks-Girardeau gas in harmonic traps [16]. A natural extension of the proposed method for generic quench settings is to join it with quantum generalised hydrodynamics to trace backward in time the quantum correlations, similarly to what recently done for the entanglement entropies and spectrum [21][22][23][24][25]. An interesting application of our result would be to discretise the field theoretical result (52) to engineer both numerically and experimentally the hydrodynamic entanglement Hamiltonian of the domain wall melting, on the lines of Refs.…”

“…Although the non-interacting nature of the underlying problem typically allows for exact lattice calculations, we rather consider its Euler hydrodynamic description where spacetime scales i, t → ∞ at fixed ratio i/t. Indeed, employing such a hydrodynamic description not only gives access to asymptotically exact results for conserved quantities [68][69][70][71][72][73] but it further allows to investigate several non-trivial properties of the model, including correlation functions [13][14][15][16] and Rényi entropies [17,[21][22][23][24], which are currently not accessible by standard lattice techniques even for the free Fermi gas in such non-homogeneous and nonequilibrium settings. Hence, following this program, the macrostate at t = 0 is given by the fermionic occupation function [77,78]…”

“…3.1 and determine the dynamics of the quantum fluctuations using quantum generalised hydrodynamics, see e.g. [21][22][23][24].…”

“…Roughly in parallel, the dynamical problem was also studied with the goal of completing such asymptotic approach with a quantum hydrodynamic theory. To date, thanks to the re-quantisation of the semi-classical evolution established by the generalised hydrodynamics [19,20], it has been possible to obtain promising results for the large-scale dynamics of the entanglement entropy [21][22][23][24][25] and to reproduce the numerical data obtained for the microscopic models with an impressive precision. Although some aspects of this emerging quantum hydrodynamic theory still remain to be clarified [26], it is a matter of fact that it provides asymptotically exact results for the entanglement dynamics, extending our analytical capabilities far beyond the current computational and conceptual limits set by standard lattice formulations.…”

“…[68][69][70][71][72][73] and in the field theory regime e.g. [11,12,23,24,[74][75][76]. In particular, it was one of the first models for which a semi-classical hydrodynamics has been formulated in the modern language [68,73], the first non-equilibrium setting for which the entanglement dynamics has been computed via quantum hydrodynamics [12], and one of the extremely rare cases for which a non-equilibrium CFT description of quantum fluctuations has been formulated [11].…”