R\'enyi entropies of generic thermodynamic macrostates in integrable systems

TL;DR

This paper investigates the behavior of Rènyi entropies in thermodynamic macrostates of integrable systems, providing methods to reconstruct driving terms from macrostate densities and analyzing specific quenches in XXZ spin chains.

Contribution

It introduces a way to derive the driving term in the TBA from macrostate densities and applies this to compute stationary Rènyi entropies after quenches in XXZ chains.

Findings

Explicit formulas for Rènyi entropies after specific quenches.

Validation of theoretical results with numerical simulations.

Analytical handling of certain limits in the entropy calculations.

Abstract

We study the behaviour of R\'enyi entropies in a generic thermodynamic macrostate of an integrable model. In the standard quench action approach to quench dynamics, the R\'enyi entropies may be derived from the overlaps of the initial state with Bethe eigenstates. These overlaps fix the driving term in the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term can be also reconstructed starting from the macrostate's particle densities. We then compute explicitly the stationary R\'enyi entropies after the quench from the dimer and the tilted N\'eel state in XXZ spin chains. For the former state we employ the overlap TBA approach, while for the latter we reconstruct the driving terms from the macrostate. We discuss in full details the limits that can be analytically handled and we use numerical simulations to check our results against the large time limit of the entanglement entropies.