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

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.