Entanglement Chern number for an extensive partition of a topological ground state

TL;DR

This paper introduces the entanglement Chern number, a new topological invariant derived from the entanglement spectrum, applicable to various topological ground states including interacting systems, providing an alternative to existing invariants.

Contribution

It proposes the entanglement Chern number as a natural, calculable topological invariant for extensive partitions, extending its applicability to time-reversal invariant and weak topological phases.

Findings

Entanglement Chern number defines a topological invariant from the entanglement spectrum.

It serves as an alternative invariant for time-reversal invariant systems.

It can be effective for interacting topological systems, unlike traditional $Z_2$ invariants.

Abstract

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an entanglement Chern number as a useful, natural, and calculable topological invariant, which is potentially relevant to various topological ground states. We show that it serves as an alternative topological invariant for time-reversal invariant systems and as a new topological invariant for a weak topological phase of a superlattice Wilson-Dirac model. In principle, the entanglement Chern number can also be effective for interacting systems such as topological insulators in contrast to $Z_2$ invariants.