Entanglement negativity in the harmonic chain out of equilibrium

TL;DR

This paper investigates entanglement in a harmonic oscillator chain driven out of equilibrium, revealing how steady-state entanglement can be understood as an average of contributions from reservoirs, with results supported by conformal field theory.

Contribution

It provides an explicit construction of the steady state and analyzes entanglement using logarithmic negativity in a non-equilibrium harmonic chain.

Findings

Steady-state entanglement is a sum of contributions from left- and right-moving excitations.

Steady-state entanglement is an average of Gibbs-state values, scalable via conformal field theory.

A local quench case shows similar averaging behavior during evolution.

Abstract

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left- and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.