Quantum group approach to steady states of boundary-driven open quantum systems

Abstract

We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on fundamental solutions of the quantum Yang-Baxter equation pertaining to quantum algebra symmetries and their quantizations (q-deformations). In particular, we facilitate a matrix-product state description, by resorting to generic spin-s infinite-dimensional solutions associated with non-compact spins, serving as ancillary degrees of freedom. After formally deriving already known solutions for the anisotropic spin-1/2 Heisenberg chain from first symmetry principles, we obtain a class of solutions belonging to interacting quantum gases with SU(N)-symmetric Hamiltonians, using a restricted set of incoherent boundary jump processes, and point out how new non-trivial generalizations emerge from twists of quantum group structures. Finally, we discuss possibilities of analytic calculation of observables by employing algebraic properties of associated auxiliary vertex operators.