Topological phase transitions at finite temperature

Abstract

The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this quantity to mixed states - known as the ensemble geometric phase (EGP) - has emerged as a robust way to describe topology at non-zero temperature. By using this quantity, we explore the nature of topology allowed for dissipation beyond a Lindblad description, to allow for coupling to external baths at finite temperatures. We introduce two main aspects to the theory of mixed state topology. First, we discover topological phase transitions as a function of the temperature T, manifesting as changes in winding number of the EGP accumulated over a closed loop in parameter space. We characterize the nature of these transitions and reveal that the corresponding non-equilibrium steady state at the transition can exhibit a nontrivial structure - contrary to previous studies where it was found to be in a fully mixed state. Second, we demonstrate that the EGP itself becomes quantized when key symmetries are present, allowing it to be viewed as a topological marker which can undergo equilibrium topological transitions at non-zero temperatures.

13 pages, 6 figures; comments welcome

References in corpus (23)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological characterization of periodically-driven quantum systems
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Helical Metal Inside a Topological Band Insulator
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topology of density matrices
• Mixed state dynamical quantum phase transition and emergent topology
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological indices for open and thermal systems via Uhlmann's phase
• Phonon-induced topological transitions and crossovers in Dirac materials
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Temperature effects in the band structure of topological insulators
• Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with Next-to-Nearest-Neighbour interactions
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Phonon-induced topological insulation
• Universalities of thermodynamic signatures in topological phases
• Topological order of mixed states in quantum many-body systems
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model

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• Many-Body Open Quantum Systems
• Robustness of topological order against disorder
• Dissipative Boundary State Preparation
• Interaction-induced topological phase transition at finite temperature
• Edge modes and symmetry-protected topological states in open quantum systems
• Electron conductance and many-body marker of a cavity-embedded topological 1D chain
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Mixed-state phase transitions in spin-Holstein models
• Lindbladian versus Postselected Non-Hermitian Topology
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Finite-temperature topological invariant for higher-order topological insulators
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Absorbance marker: Detection of quantum geometry and spread of Wannier function in disordered 2D semiconductors
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions