Quantum information dynamics in multipartite integrable systems

TL;DR

This paper develops an exact theoretical framework to understand quantum information dynamics in integrable many-body systems, specifically quantifying entanglement evolution between non-complementary regions after a quench.

Contribution

It introduces a quasiparticle-based approach to predict the time evolution of logarithmic negativity in integrable systems, linking it to Rènyi mutual information in the long-time limit.

Findings

Logarithmic negativity is proportional to Rènyi mutual information with index 1/2 in the scaling limit.

The framework is validated for free-fermion and free-boson models.

Applicable to any interacting integrable system.

Abstract

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the R\'enyi mutual information with R\'enyi index $\alpha=1/2$. We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.