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.

36 pages

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Cited by in corpus (18)

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• The thermodynamic cost of driving quantum systems by their boundaries
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• Matrix product solutions of boundary driven quantum chains
• Infinitely dimensional Lax structure for one-dimensional Hubbard model
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Charge and spin current statistics of the open Hubbard model with weak coupling to the environment
• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
• Integrability of open boundary driven quantum circuits
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Continuous phase-space methods on discrete phase spaces
• Integrability versus chaos in the steady state of many-body open quantum systems
• Defect production in quench from current-carrying non-equilibrium state
• Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators
• Nonequilibrium phases and quantum correlations in synthetic transport models