Exact solution for a diffusive nonequilibrium steady state of an open quantum chain

TL;DR

This paper derives an exact analytical description of the nonequilibrium steady state in a quantum XX chain with dephasing and boundary driving, revealing diffusive behavior, long-range correlations, and a phase transition.

Contribution

It provides an exact solution for the steady state of a quantum chain under nonequilibrium conditions, including correlation functions for arbitrary driving strength.

Findings

Magnetization profile and spin current are diffusive.

Long-range correlations appear in the steady state.

A phase transition occurs from ballistic to diffusive transport at zero dephasing.

Abstract

We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. Spin-spin correlation function on the other hand has long-range correlations which though decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.