Entanglement and inversion symmetry in topological insulators

Abstract

Topological band insulators are usually characterized by symmetry-protected surface modes or quantized linear-response functions (like Hall conductance). Here we present a way to characterize them based on certain bulk properties of just the ground-state wave function, specifically, the properties of its entanglement spectrum. We prove that whenever protected surface states exist, a corresponding protected ``mode'' exists in the entanglement spectrum as well. Besides this, the entanglement spectrum sometimes succeeds better at indicating topological phases than surface states. We discuss specifically the example of insulators with inversion symmetry which is found to act as an antiunitary symmetry on the entanglement spectrum. A Kramers degeneracy can then arise even when time-reversal symmetry is absent. This degeneracy persists for interacting systems. The entanglement spectrum is therefore a promising tool to characterize topological band insulators and superconductors beyond the free-particle approximation.