Exact Nonequilibrium Steady State of Open <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math> Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> 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 the 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.

Topics & Concepts