title: Exact matrix product solution for the boundary-driven Lindblad XXZ chain.
abstract: We demonstrate that the exact nonequilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the nonequilibrium density matrix where the matrices satisfy a quadratic algebra. This algebra turns out to be related to the quantum algebra U(q)[SU(2)]. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to nonvanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.
authors.affiliation: Institut Jean Lamour, Department P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France.
authors.forename: D
authors.initials: D
authors.lastname: Karevski
authors.affiliation: Dipartimento di Fisica, Università di Firenze, via Sansone 1, 50019 Sesto Fiorentino Firenze, Italy and Max Planck Institute for Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
authors.forename: V
authors.initials: V
authors.lastname: Popkov
authors.affiliation: Institute of Complex Systems II, Forschungszentrum Jülich, 52428 Jülich, Germany.
authors.forename: G M
authors.initials: GM
authors.lastname: Schütz