Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect

TL;DR

This paper introduces a many-body Z2 topological invariant for quantum spin Hall insulators that does not depend on single-particle band structures, using a Wilson-loop approach linked to time-reversal symmetry.

Contribution

It develops a many-body topological invariant for quantum spin Hall states, extending topological classification beyond single-particle frameworks.

Findings

Defines a many-body Z2 invariant as a topological obstruction.

Expresses the invariant as a quantized Wilson-loop of the SU(2) Berry gauge field.

Applicable to interacting systems without single-particle band structures.

Abstract

We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson-loop of the SU(2) Berry gauge field, which is quantized due to the time-reversal symmetry.