Entanglement of Stationary States in the Presence of Unstable Quasiparticles

TL;DR

This paper investigates how unstable quasiparticles influence entanglement entropy dynamics after a quantum quench in integrable systems, revealing a minimum entropy growth rate and a scale separation linked to conformal field theory predictions.

Contribution

It introduces a detailed analysis of entanglement entropy and growth rates considering unstable quasiparticles, highlighting a scale separation and a double-plateau structure in the dynamics.

Findings

Entropy growth rate has a global minimum at the unstable particle threshold.

A scale separation exists between free fermion and interacting regimes.

Double-plateau structure in functions related to entropy dynamics.

Abstract

The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes $K(\theta)$ become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.