Exact hydrodynamic description of symmetry-resolved R\'enyi entropies after a quantum quench

TL;DR

This paper provides an exact hydrodynamic framework to analyze the non-equilibrium evolution of symmetry-resolved Rnyi entropies in a one-dimensional free fermion gas after a quantum quench, revealing detailed entanglement dynamics.

Contribution

It introduces a precise hydrodynamic description of symmetry-resolved entropies in quantum quenches, extending previous total entanglement results to symmetry sectors.

Findings

Charged moments grow logarithmically at half system

Entropy tends to distribute equally among symmetry sectors over time

Deviations from equipartition decrease quadratically with inverse total entropy

Abstract

We investigate the non-equilibrium dynamics of the symmetry-resolved R\'enyi entropies in a one-dimensional gas of non-interacting spinless fermions by means of quantum generalised hydrodynamics, which recently allowed to obtain very accurate results for the total entanglement in inhomogeneous quench settings. Although our discussion is valid for any quench setting accessible with quantum generalised hydrodynamics, we focus on the case of a quantum gas initially prepared in a bipartite fashion and subsequently let evolve unitarily with a hopping Hamiltonian. For this system, we characterise the symmetry-resolved R\'enyi entropies as function of time $t$ and of the entangling position $x$ along the inhomogeneous profile. We observe an asymptotic logarithmic growth of the charged moments at half system and an asymptotic restoration of equipartition of entropy among symmetry sectors with deviations which are proportional to the square of the inverse of the total entropy.