Entanglement negativity in a nonequilibrium steady state

TL;DR

This paper investigates entanglement measures in a nonequilibrium steady state of a free-fermion chain, revealing how negativity and mutual information scale with system size and differ in their informational content.

Contribution

It analytically derives the scaling prefactors of entanglement negativity and Rènyi mutual information in a nonequilibrium steady state, highlighting their differences.

Findings

Negativity and mutual information scale logarithmically with system size.

Prefactors for negativity and mutual information differ, indicating they capture different aspects of entanglement.

Logarithmic growth of negativity during evolution is determined by the steady-state prefactor.

Abstract

We study entanglement properties in a nonequilibrium steady state of a free-fermion chain, that emerges after connecting two half-chains prepared at different temperatures. The entanglement negativity and the R\'enyi mutual information between two adjacent intervals scale logarithmically in the system size, with prefactors that we calculate analytically as a function of the bath temperatures. In particular, we show that the negativity and the R\'enyi mutual information with index $\alpha=1/2$ are described by different prefactors, and thus the two quantities provide inequivalent information about the state. Furthermore, we show that the logarithmic growth of the negativity during time evolution is also governed by the steady-state prefactor.