Measuring post-quench entanglement entropy through density correlations

TL;DR

This paper investigates how post-quench entanglement entropy in a one-dimensional fermionic system can be measured through density correlations, revealing a method to connect density fluctuations to entropy dynamics after a quantum quench.

Contribution

It introduces a novel approach to estimate entanglement entropy from density correlations shortly after a quantum quench in integrable fermionic systems.

Findings

Excellent agreement between bosonic entropy and steady state entanglement entropy.

Method effectively maps the system to non-interacting bosons at small waiting times.

Density correlation analysis provides a practical way to measure entanglement entropy.

Abstract

Following a sudden change of interactions in an integrable system of one-dimensional fermions, we analyze the dependence of the static structure factor on the observation time after the quantum quench. At small waiting times after the quench, we map the system to non-interacting bosons such that we are able to extract their occupation numbers from the Fourier transform of the density-density correlation function, and use these to compute a bosonic entropy from a diagonal ensemble. By comparing this bosonic entropy with the asymptotic steady state entanglement entropy per fermion computed with exact diagonalization we find excellent agreement.