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arXiv:2606.07736

Exact metastability in a class of driven-dissipative quantum many-body systems

David D. Noachtar, Aashish A. Clerk

quant-phcond-mat.stat-mechSubmitted Jun 5, 2026• Announced Jun 9, 2026• 0 citations
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Abstract

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.

Comments
19 + 14 pages, 9 + 3 figures, 0 + 1 tables

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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.
Driven-dissipative collective spin systems can host several long-lived metastable states; rare switching between them governs slow relaxation and first-order dissipative phase transitions associated with changes in the dominant stationary state. In the companion Letter [arXiv:2604.15091], we introduced a quantum instanton framework based on exact quasiprobability dynamics to describe this switching and illustrated it with a minimal model possessing a simplifying symmetry. Here we develop its numerical implementation, combining collocation and shooting methods, and apply it to two microscopically motivated systems: the Lipkin-Meshkov-Glick model with purely collective dissipation and the cooperative resonance fluorescence with collective and local dissipation. By determining the leading exponential scaling of switching rates between metastable attractors, we predict the stationary magnetization, the first-order dissipative phase-transition point, and the exponential scaling of slow relaxation rates. These predictions agree with quantum master-equation calculations and an exact analytical result for the second model without dephasing. We also examine how the choice of quasiprobability representation affects numerical convergence and find that the alternative semiclassical Wigner approach, based on Gaussian truncation, has varying accuracy across models and parameter regimes. These results substantiate the framework's applicability to experimentally relevant collective spin systems with both collective and local dissipation.
Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry, which most directly manifests itself in a doubled version of the original system prepared in an appropriate entangled thermofield double state. This hidden time-reversal symmetry has a direct operational utility: it provides a general method for finding exact solutions of nontrivial steady states. Special cases of this approach include the coherent quantum absorber and complex-P function methods from quantum optics. We also show that hidden time-reversal symmetry has observable consequences even in single-system experiments, and can be broken by the nontrivial combination of nonlinearity, thermal fluctuations, and driving. To illustrate our ideas, we analyze concrete examples of driven qubits and nonlinear cavities. These systems exhibit hidden time-reversal symmetry but not conventional detailed balance.
Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions.We show that such systems can nonetheless exhibit a hidden time-reversal symmetry, which most directly manifests itself in a doubled version of the original system prepared in an appropriate entangled thermofield double state.This hidden time-reversal symmetry has a direct operational utility: it provides a general method for finding exact solutions of nontrivial steady states.Special cases of this approach include the coherent quantum absorber and complex-P function methods from quantum optics.We also show that hidden time-reversal symmetry has observable consequences even in single-system experiments, and can be broken by the nontrivial combination of nonlinearity, thermal fluctuations, and driving.To illustrate our ideas, we analyze concrete examples of driven qubits and nonlinear cavities.These systems exhibit hidden time-reversal symmetry but not conventional detailed balance.
The dissipative transverse-field Ising (TFI) model provides a paradigmatic setting for nonequilibrium quantum many-body physics. We show that a class of boundary-driven TFI models subject to dissipation at only one boundary possesses hidden time-reversal symmetry, which enables an exact construction of their nonequilibrium steady states. The solution admits a matrix-product representation and defines a nonequilibrium partition function from which steady-state observables can be evaluated efficiently. We use the exact solution to characterize the microscopic structure of the steady state through its z-magnetization and two-point correlations. A striking feature is that the local field at the dissipative boundary governs the spatial organization of the steady state throughout the chain. The steady state typically exhibits boundary-localized magnetization profiles and exponentially decaying correlations, whose characteristic length scales are set by the dissipative boundary. In the weak-driving limit, suitably tuned boundary fields can reorganize the NESS into a delocalized single-interface structure, giving rise to long-range correlations that decay linearly with distance.
Collective spin systems -- driven-dissipative spin ensembles whose unitary and dissipative processes act uniformly on all spins, allowing their dynamics to be described as a single macrospin -- play an important role in atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple long-lived metastable states that ultimately relax to a unique most probable state. This dominant state can change with a control parameter, leading to first-order phase transitions. We develop a real-time instanton approach based on quantum quasiprobability dynamics that captures the stationary state in the large-spin limit and the asymptotic scaling of relaxation rates. We further show that these features are not accurately described by the previously applied semiclassical Wigner approach due to its neglect of non-Gaussian fluctuations.
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.