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

Abstract

In this study, we discuss a 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 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 because of 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 noninteracting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions. Published by the American Physical Society 2024