Finite-temperature topological invariant for interacting systems

Abstract

We generalize the Ensemble Geometric Phase (EGP), recently introduced to classify the topology of density matrices, to finite-temperature states of interacting systems in one spatial dimension (1D). This includes cases where the gapped ground state has a fractional filling and is degenerate. At zero temperature the corresponding topological invariant agrees with the well-known invariant of Niu, Thouless and Wu. We show that its value at finite temperatures is identical to that of the ground state below some critical temperature $T_c$ larger than the many-body gap. We illustrate our result with numerical simulations of the 1D extended super-lattice Bose-Hubbard model at quarter filling. Here a cyclic change of parameters in the ground state leads to a topological charge pump with fractional winding $\nu =1/2$. The particle transport is no longer quantized when the temperature becomes comparable to the many-body gap, yet the winding of the generalized EGP is.

arXiv comment10 pages, 5 figures

References in corpus (34)

• Topological Insulators
• Berry Phase Effects on Electronic Properties
• The density-matrix renormalization group in the age of matrix product states
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Zoo of quantum-topological phases of matter
• The Quantum-Mechanical Position Operator in Extended Systems
• Electron Localization in the Insulating State
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Topology by dissipation
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Topology of density matrices
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Quantum-Mechanical Position Operator and Localization in Extended Systems
• Devil's staircases and supersolids in a one-dimensional dipolar Bose gas
• Quantum response of dephasing open systems
• Lightcone renormalization and quantum quenches in one-dimensional Hubbard models
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Reservoir-induced Thouless pumping and symmetry protected topological order in open quantum chains
• Quantum phase diagram of the generalized ionic Hubbard model for AB${}_n$ chains
• Finite-size corrections to quantized particle transport in topological charge pumps
• Topological order of mixed states in quantum many-body systems
• Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
• Classification of Mixed State Topology in One Dimension
• Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss
• Berry phases in superconducting transitions
• Absence of topology in Gaussian mixed states of bosons
• Quantized transport induced by topology transfer between coupled one-dimensional lattice systems

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• Quantisation and its breakdown in a Hubbard-Thouless pump
• Symmetry classes of open fermionic quantum matter
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Interactions enable Thouless pumping in a nonsliding lattice
• Many-Body Open Quantum Systems
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Topological phase transitions at finite temperature
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• 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
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Quantized transport induced by topology transfer between coupled one-dimensional lattice systems
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Finite-temperature topological invariant for higher-order topological insulators
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Topological states of generalized dissipative Majorana wires
• Comparison of finite-temperature topological indicators based on Uhlmann connection