Exact nonequilibrium steady state of open XXZ/XYZ spin-1/2 chain with Dirichlet boundary conditions

TL;DR

This paper derives an exact description of the nonequilibrium steady state for an open XYZ spin-1/2 chain under strong dissipation, revealing connections to integrable models and quantum groups.

Contribution

It introduces a novel matrix product ansatz with site-dependent Lax operators for the XYZ chain in the Zeno limit, extending the algebraic structure of quantum integrability.

Findings

Exact steady state expressed via matrix product ansatz.

Lax operators satisfy linear recurrence relations generalizing quantum group relations.

Links between dissipative steady states and integrable models with edge magnetic fields.

Abstract

We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, described by Lindblad master equation. The nonequilibrium steady state is expressed in terms of a matrix product ansatz using novel site-dependent Lax operators. The components of Lax operators satisfy a simple set of linear recurrence equations that generalize the defining algebraic relations of the quantum group $U_q(sl_2)$. We reveal connection between the nonequilibrium steady state of the nonunitary dynamics and the respective integrable model with edge magnetic fields, described by coherent unitary dynamics.