Exact nonequilibrium steady state of a strongly driven open XXZ chain

TL;DR

This paper presents an exact analytical solution for the non-equilibrium steady state of a driven XXZ spin chain, revealing detailed physical properties and correlations in a nonperturbative framework.

Contribution

It introduces a novel ladder-tensor-network ansatz for the exact steady state of a driven XXZ chain, extending previous perturbative results to a fully nonperturbative regime.

Findings

Cosine spin profiles in the isotropic case

Spin current scales as 1/n^2

Presence of long-range correlations in the steady state

Abstract

An exact and explicit ladder-tensor-network ansatz is presented for the non-equilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges of the chain only. We show that the steady-state density operator of a finite system of size n is - apart from a normalization constant - a polynomial of degree 2n-2 in the coupling constant. Efficient computation of physical observables is faciliated in terms of a transfer operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n^2 scaling of the spin current, and long-range correlations in the steady state. This is a fully nonperturbative extension of a recent result [Phys. Rev. Lett. 106, 217206 (2011)].