Solvable quantum nonequilibrium model exhibiting a phase transition and a matrix product representation

TL;DR

This paper analyzes a 1D quantum XX chain under nonequilibrium conditions, providing an exact solution for the steady state, revealing a phase transition, and demonstrating a matrix product operator representation with fixed matrices.

Contribution

It extends the analytical solution of the nonequilibrium steady state to arbitrary parameters and shows it can be represented by a fixed-dimension matrix product operator.

Findings

Explicit evaluation of all correlation functions.

Identification of a nonequilibrium phase transition at zero dephasing.

Steady state is weakly correlated and non-Gaussian.

Abstract

We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech., L05002 (2010)] is extended to arbitrary coupling constants, driving and homogeneous magnetic field. All one, two and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not gaussian. Nevertheless, in the thermodynamic and weak-driving limit it is only weakly correlated and can be described by a matrix product operator ansatz with matrices of fixed dimension 4. A nonequilibrium phase transition at zero dephasing is also discussed. It is suggested that the scaling of the relaxation time with the system size can serve as a signature of a nonequilibrium phase transition.