Topological order of mixed states in quantum many-body systems

Abstract

Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical ensembles. For a large class of quasi-thermal states, which can be realized as thermal states of some quasi-local Hamiltonian, we generalize earlier definitions of density matrix topology to generic many-body systems with strong correlations. We point out that the robustness of topological order, defined as a pattern of long-range entanglement, depends crucially on the perturbations under consideration. While it is intrinsically protected against local perturbations of arbitrary strength in an infinite closed quantum system, purely local perturbations can destroy topological order in open systems coupled to baths if the coupling is sufficiently strong. We discuss our classification scheme using the finite-temperature quantum Hall states and point out that the classical Hall effect can be understood as a finite temperature topological phase.

12 pages, 6 figures

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Cited by in corpus (12)

• Symmetry protected topological phases under decoherence
• Topological phase transitions at finite temperature
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Symmetry classes of dissipative topological insulators with edge dark state
• Mixed-state phase transitions in spin-Holstein models
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system