Exact descriptions of boundary-driven quantum spin chains using hidden time-reversal symmetry

Non-equilibrium steady states of driven-dissipative quantum systems can exhibit a variety of fascinating phenomena. In the case where interactions are strong, numerical simulation is often difficult, hence having exactly solvable models is especially helpful. Very recent work has shown that a kind of quantum detailed balance, so-called ‘hidden time reversal symmetry’ (hTRS) [1,2] can be used to derive exact descriptions of many-body dissipative models with collective interactions. Here, we show this approach can be used in a far wider class of systems: a class of one-dimensional interacting spin chains with boundary driving and dissipation, where the steady states have a non-vanishing excitation current. The method allows us to find new solvable models, and also provides new insights into models that were known to be solvable using other methods. Our approach also allows us to identify a surprising class of observable Onsager correlation function symmetries. Our results are directly relevant to state-of-the-art quantum simulation platforms, e.g. recent experiments with superconducting quantum circuits [3].[1] Roberts, David, and A. A. Clerk. 2023. “Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution.” Physical Review Letters 130 (6): 063601.

[2] Roberts, David, and Aashish A. Clerk. 2023. “Exact Solution of an Infinite-Range, Non-Collective Dissipative Transverse-Field Ising Model.” http://arxiv.org/abs/2307.06946.

[3] Mi, X., A. A. Michailidis, S. Shabani, et al. 2023. “Stable Quantum-Correlated Many Body States via Engineered Dissipation.” http://arxiv.org/abs/2304.13878.