Symmetry-protected entangling boundary zero modes in crystalline topological insulators

Abstract

Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.

88 pages, 16 figures, Table of contents added, published version in JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physics

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• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• CPT theorem and classification of topological insulators and superconductors
• Topology and entanglement in quench dynamics
• Entanglement negativity in free-fermion systems: An overlap matrix approach
• Embedded Topological Insulators
• Disorder-induced topology in quench dynamics
• Protected Gapless Edge States In Trivial Topology
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Two-dimensional Paired Topological Superfluids of Rydberg Fermi Gases
• Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum