Steady-state topological order is defined via degeneracy and entropy in open-system Liouvillians, with models showing exponential splitting but algebraically closing gaps.
Topologically Ordered Steady States in Open Quantum Systems
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abstract
The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Liouvillians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the steady-state topological degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of steady-state topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.
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UNVERDICTED 3representative citing papers
Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.
Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.
citing papers explorer
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Steady-state topological order
Steady-state topological order is defined via degeneracy and entropy in open-system Liouvillians, with models showing exponential splitting but algebraically closing gaps.
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Topologically Ordered Steady States in Open Quantum Systems
Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.
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Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.