The Z2-anomaly and boundaries of topological insulators

TL;DR

This paper uncovers a novel Z2-anomaly in topological insulators related to charge conservation, revealing fundamental constraints on their edge theories and robustness against interactions and disorder.

Contribution

It introduces a new Z2-anomaly in topological insulators' boundary theories, linking anomalies to physical properties and robustness of these materials.

Findings

Divergence in a 2-point correlation function indicates the Z2-anomaly.

Flux insertion causes ground state orthogonality, independent of flux rate.

Anomaly persists despite disorder, constraining low-energy theories.

Abstract

We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a novel Z2-anomaly associated with charge conservation. The anomaly is manifested through a 2-point correlation function involving creation and annihilation operators on two decoupled boundaries. Although charge conservation on each boundary requires this quantity to vanish, we find that it diverges. A corollary result is that under an insertion of a flux quantum the ground state evolves to an exactly orthogonal state independent of the rate at which the flux is inserted. The anomaly persists in the presence of disorder and imposes sharp restrictions on possible low energy theories. Being formulated in a many-body, field theoretical language, the anomaly allows to test the robustness of topological insulators to interactions in a concise way.