A matrix product solution for a nonequilibrium steady state of an XX chain

TL;DR

This paper presents an exact matrix product state solution for the nonequilibrium steady state of a finite XX spin chain coupled to reservoirs, revealing that only nearest neighbor z-z correlations are non-zero.

Contribution

The authors derive a fixed-dimension matrix product state representation for the steady state of an XX chain with boundary reservoirs, providing explicit calculations of observables.

Findings

All connected correlations except nearest neighbor z-z are zero.

Explicit matrix representation of dimension 4 is independent of chain length.

Steady state expectations are analytically evaluated.

Abstract

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from nearest neighbor z-z, are zero.