Growth of R\'enyi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture

TL;DR

This paper reveals that the growth rate of Rènyi entropies after a quantum quench in integrable models can be exactly calculated using a spacetime duality, linking out-of-equilibrium dynamics to equilibrium properties.

Contribution

It introduces a novel spacetime duality approach to determine Rènyi entropy growth rates in integrable models, providing explicit formulas and highlighting limitations of the quasiparticle picture.

Findings

The slope of Rènyi entropies equals a stationary entropy density in a dual model.

An explicit exact formula for the Rènyi entropy growth rate in integrable models is derived.

The quasiparticle picture applies only in the von Neumann entropy limit.

Abstract

R\'enyi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out-of-equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterisation is a key objective of current research. Here we show that the slope of R\'enyi entropies can be determined by means of a spacetime duality transformation. In essence, we argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement is expressed as an equilibrium quantity. We use this observation to find an explicit exact formula for the slope of R\'enyi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. Interestingly, this formula can be understood in terms of a quasiparticle picture only in the von Neumann limit.