Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors

Abstract

In this study, we discuss a new type of bulk-boundary correspondence which holds for topological insulators and superconductors when the parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these systems, even when the bulk topology is nontrivial, the edge spectrum is generally gapped, and thus the conventional bulk-boundary correspondence does not hold. We find that, instead of the edge spectrum, the single-particle entanglement spectrum becomes gapless when the bulk topology is nontrivial: i.e., the $\text{bulk-entanglement}$ $\text{spectrum}$ $\text{correspondence}$ holds in $PT$- and/or $PC$-symmetric topological insulators and superconductors. After showing the correspondence using $K$-theoretic approach, we provide concrete models for each symmetry class up to three dimensions where nontrivial topology due to $PT$ and/or $PC$ is expected. An implication of our results is that, when the bulk topology under $PT$ and/or $PC$ symmetry is nontrivial, the non-interacting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions.

arXiv comment22 pages, 9 figures

References in corpus (45)

• Topological Insulators
• Topological insulators and superconductors
• 2D materials and van der Waals heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Calculation of reduced density matrices from correlation functions
• Topological nodal line semimetals with and without spin-orbital coupling
• Graphene Bilayers with a Twist
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Inversion Symmetric Topological Insulators
• Topology of crystalline insulators and superconductors
• Entanglement spectrum of topological insulators and superconductors
• Fragile Topology and Wannier Obstructions
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Stability of Fermi Surfaces and K-Theory
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Topological Classification and Stability of Fermi Surfaces
• Entanglement in solvable many-particle models
• Topological Euler class as a dynamical observable in optical lattices
• Observation of non-Abelian topological semimetals and their phase transitions
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Geometric approach to fragile topology beyond symmetry indicators
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Topological Blount's theorem of odd-parity superconductors
• Mode-Wise Entanglement of Gaussian States
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Multicellularity of delicate topological insulators
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
• Topological Euler insulators
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps

Cited by in corpus (3)

• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Breakdown of the symmetry constraint in a Floquet topological insulator