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arXiv:2407.12750 · Physical Review Letters

Hidden Time Reversal in Driven X X Z Spin Chains: Exact Solutions and New Dissipative Phase Transitions

Mingxing Yao, Andrew Lingenfelter, Ron Belyansky, David C K Roberts, Aashish A. Clerk

Published Apr 4, 2025• 5 citations
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Abstract

We show that several models of interacting XXZ spin chains subject to boundary driving and dissipation possess a subtle kind of time-reversal symmetry, making their steady states exactly solvable. We focus on a model with a coherent boundary drive, showing that it exhibits a unique continuous dissipative phase transition as a function of the boundary drive amplitude. This transition has no analog in the bulk closed system or in incoherently driven models. We also show the steady-state magnetization exhibits a surprising fractal dependence on interaction strength, something previously associated with less easily measured infinite-temperature transport quantities (the Drude weight). Our exact solution also directly yields driven-dissipative double-chain models that have pure, entangled steady states that are current carrying.

DOI
10.1103/physrevlett.134.130404

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Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
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