Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2011.02148 · PRX Quantum

Hidden Time-Reversal Symmetry, Quantum Detailed Balance and Exact Solutions of Driven-Dissipative Quantum Systems

David Roberts, Andrew Lingenfelter, A.A. Clerk

Published Jun 8, 2021• 38 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/prxquantum.2.020336

Related papers

Hidden Time-Reversal Symmetry, Quantum Detailed Balance and Exact Solutions of Driven-Dissipative Quantum Systems

David C K Roberts, Andrew Lingenfelter, Aashish A. Clerk

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.

•Jun 8, 2021•27 citations

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

David D. Noachtar, Aashish A. Clerk

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.

quant-pharXiv:2606.07736•Jun 9, 2026•0 citations

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

Mingxing Yao, Andrew Lingenfelter, Ron Belyansky +2 more

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.

arXiv:2407.12750•Physical Review Letters•Apr 4, 2025•5 citations

Exact steady states of interacting driven dissipative fermionic systems with hidden time-reversal symmetry

Andrew Lingenfelter, Aashish A. Clerk

We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every site. Our exact solution is found by generalizing the coherent quantum absorber technique to fermionic systems, and our result establishes the existence of hidden time-reversal symmetry in driven-dissipative fermionic models. The steady state exhibits a first order phase transition in the particle density, with the resulting jump discontinuity in density persisting even for finite dissipation rates. A mean-field description of the model exhibits a bistable regime that encompasses the first-order transition line yet which fails to accurately predict its precise location via a Maxwell construction. We also show that the model's hidden time-reversal symmetry results in an Onsager symmetry of certain two-time correlation functions.

quant-pharXiv:2605.10846•May 12, 2026•0 citations

Exact solution of a boundary-driven transverse-field Ising model with hidden time-reversal symmetry

Xudong Liu, Shu Chen

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.

quant-pharXiv:2609.28994•Sep 25, 2026•0 citations

Time-reversal symmetry breaking and emergence in driven-dissipative Ising models

Daniel A. Paz, Mohammad F. Maghrebi

Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators under time-reversal transformation, that overlap with the order parameter. Remarkably, however, a modified form of the FDR as well as TRS still holds, but with drastic consequences for the correlation and response functions as well as the Onsager reciprocity relations. Finally, we find that, at criticality, TRS remains broken even in the weakly-dissipative limit.

arXiv:2105.12747•SciPost Physics•Feb 17, 2022•4 citations
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.
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.
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.
We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every site. Our exact solution is found by generalizing the coherent quantum absorber technique to fermionic systems, and our result establishes the existence of hidden time-reversal symmetry in driven-dissipative fermionic models. The steady state exhibits a first order phase transition in the particle density, with the resulting jump discontinuity in density persisting even for finite dissipation rates. A mean-field description of the model exhibits a bistable regime that encompasses the first-order transition line yet which fails to accurately predict its precise location via a Maxwell construction. We also show that the model's hidden time-reversal symmetry results in an Onsager symmetry of certain two-time correlation functions.
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.
Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators under time-reversal transformation, that overlap with the order parameter. Remarkably, however, a modified form of the FDR as well as TRS still holds, but with drastic consequences for the correlation and response functions as well as the Onsager reciprocity relations. Finally, we find that, at criticality, TRS remains broken even in the weakly-dissipative limit.