Hydrodynamics of quantum entropies in Ising chains with linear dissipation

TL;DR

This paper develops a hydrodynamic description of quantum entropies and correlations in dissipative Ising chains after a quench, revealing universal dynamics and the impact of dissipation on mutual information.

Contribution

It derives an analytical hydrodynamic formula for entropy dynamics in dissipative noninteracting systems, confirming a conjecture and elucidating dissipation effects on quantum correlations.

Findings

Mutual information grows then decreases, vanishing at long times.

Entropy-related quantities follow a hydrodynamic formula in the weak dissipation limit.

Universal features of correlation dynamics are demonstrated in dissipative Ising chains.

Abstract

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 R\'enyi 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.