Steady-state topological order

Abstract

We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize them by complementary approaches based on topological degeneracy of steady states, topological entropy, and dissipative gauge theory. Whereas the (Liouvillian) level splitting between topologically degenerate steady states is exponentially small with respect to the system size, the Liouvillian gap between the steady states and the rest of the spectrum decays algebraically as the system size grows, and closes in the thermodynamic limit. It is shown that steady-state topological order remains definable in the presence of (Liouvillian) gapless modes. The topological phase transition to the trivial phase, where the topological degeneracy is lifted, is accompanied by gapping out the gapless modes. Our work offers a toolbox for investigating open-system topology of steady states.

arXiv comment33 pages, 17 figures. Joint submission with arXiv:2306.12482

References in corpus (43)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Edge states and topological invariants of non-Hermitian systems
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Topological quantum memory
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Zoo of quantum-topological phases of matter
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Preparation of Entangled States by Quantum Markov Processes
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Topology by Dissipation in Atomic Quantum Wires
• Dissipative preparation of entanglement in optical cavities
• Ground state entanglement and geometric entropy in the Kitaev's model
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Topological multicritical point in the Toric Code and 3D gauge Higgs Models
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Entanglement and topological entropy of the toric code at finite temperature
• Quantum memories based on engineered dissipation
• Topological Order at Non-zero Temperature
• Topological order in a 3D toric code at finite temperature
• Quantum criticality under decoherence or weak measurement
• Freezing in Ising Ferromagnets
• Scalable Dissipative Preparation of Many-Body Entanglement
• Average Symmetry-Protected Topological Phases
• Adiabatic Preparation of Topological Order
• String and Membrane condensation on 3D lattices
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
• Diagnosing Deconfinement and Topological Order
• Intrinsic Mixed-state Topological Order
• Symmetry protected topological phases under decoherence
• Classification of phases for mixed states via fast dissipative evolution
• Topological order and topological entropy in classical systems
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Dissipative Boundary State Preparation
• Generalized Toric Codes Coupled to Thermal Baths
• Quantum robustness and phase transitions of the 3D Toric Code in a field
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
• Topologically Ordered Steady States in Open Quantum Systems
• Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space

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• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Holographic duality between bulk topological order and boundary mixed-state order
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout