Absence of topology in Gaussian mixed states of bosons

Abstract

In a recent paper [Bardyn et al. Phys. Rev. X 8, 011035 (2018)], it was shown that the generalization of the many-body polarization to mixed states can be used to construct a topological invariant which is also applicable to finite-temperature and non-equilibrium Gaussian states of lattice fermions. The many-body polarization defines an ensemble geometric phase (EGP) which is identical to the Zak phase of a fictitious Hamiltonian, whose symmetries determine the topological classification. Here we show that in the case of Gaussian states of bosons the corresponding topological invariant is always trivial. This also applies to finite-temperature states of bosons in lattices with a topologically non-trivial band-structure. As a consequence there is no quantized topological charge pumping for translational invariant bulk states of non-interacting bosons.

arXiv comment7 pages, 1 figure

References in corpus (23)

• Non-Abelian Anyons and Topological Quantum Computation
• Berry Phase Effects on Electronic Properties
• Gaussian Quantum Information
• 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
• The Quantum-Mechanical Position Operator in Extended Systems
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Electron Localization in the Insulating State
• Topology by dissipation
• Topological charge pumping in a one-dimensional optical lattice
• 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
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Quantum response of dephasing open systems
• Reservoir-induced Thouless pumping and symmetry protected topological order in open quantum chains
• Classification of Mixed State Topology in One Dimension
• Scaling of polarization amplitude in quantum many-body systems in one dimension

Cited by in corpus (9)

• Symmetry classes of open fermionic quantum matter
• Many-Body Open Quantum Systems
• Finite-temperature topological invariant for interacting systems
• Topological phase transitions at finite temperature
• Chern number and Berry curvature for Gaussian mixed states of fermions
• Electron conductance and many-body marker of a cavity-embedded topological 1D chain
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system