Entanglement evolution and generalised hydrodynamics: noninteracting systems

TL;DR

This paper extends the quasiparticle picture within generalized hydrodynamics to describe entanglement evolution after inhomogeneous quenches in noninteracting systems, providing exact predictions for various initial states.

Contribution

It generalizes the quasiparticle approach to inhomogeneous quenches in noninteracting systems using generalized hydrodynamics, offering exact entanglement predictions.

Findings

Entanglement entropy is additive for quasistationary initial states.

Exact entanglement predictions are possible for low-entangled initial states.

Additivity of entanglement entropy breaks down for non-quasistationary states.

Abstract

The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.