Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum

Abstract

We have studied extensively the band crossing patterns of the bulk entanglement spectrum (BES) for various lattice Chern insulators. We find that only partitions with dual symmetry can have either stable nodal-lines or nodal-points in the BES when the system is in the topological phase of a nonzero Chern number. By deforming the Hamiltonian to lift the accidental symmetry, one can see that only nodal points are robust. They thus should bear certain topological characteristics of the BES. By studying the band crossing patterns in details we conclude that the topological characteristics of the BES are inherited from the topological order of the underlying Chern insulators and the former can have more refined topological structures. We then propose the conjecture that the sum of the vorticities in the BES in a properly chosen reduced Brillouin zone equals the Chern number of the underlying Chern insulator. This relation is beyond the usual classification scheme of topological insulators/superconductors.

arXiv comment19 pages, 32 figures; v3: revised with various improvements, version to appear in PRB

References in corpus (30)

• Topological Insulators
• Topological insulators and superconductors
• 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
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Calculation of reduced density matrices from correlation functions
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• Classification of Topological Insulators and Superconductors
• Density-Matrix Spectra of Solvable Fermionic Systems
• Entanglement entropy and the Berry phase in solid states
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Entanglement entropy of integer Quantum Hall states
• Entanglement spectrum and Wannier center flow of the Hofstadter problem
• Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State
• Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology
• Critical entanglement spectrum of one-dimensional symmetry protected topological phases
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Entanglement Chern number for an extensive partition of a topological ground state
• Entanglement Spectrum of a Random Partition: Connection with the Localization Transition
• Tensor Network Implementation of Bulk Entanglement Spectrum
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Bulk Entanglement Spectrum in Gapped Spin Ladders
• Topologically distinct critical theories emerging from the bulk entanglement spectrum of integer quantum Hall states on a lattice
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Manifestations of topological band crossings in bulk entanglement spectrum: An analytical study for integer quantum Hall states

Cited by in corpus (1)

• Invariance of topological indices under Hilbert space truncation