Instanton effects in lattice models of bosonic symmetry-protected topological states

TL;DR

This paper investigates how instanton effects and discrete Berry phases in lattice models reveal the microscopic origins of topological theta-terms in bosonic SPT states, linking microscopic instantons to universal boundary phenomena.

Contribution

It provides a microscopic lattice perspective on instanton effects and Berry phases that encode the topological theta-term in bosonic SPT states.

Findings

Identification of discrete Berry phases in lattice models

Physical interpretation of Berry phases as instanton effects

Connection between microscopic instantons and topological properties

Abstract

Bosonic symmetry-protected topological (SPT) states are gapped disordered phases of matter possessing symmetry-preserving boundary excitations. It has been proposed that, at long wavelengths, the universal properties of an SPT system are captured by an effective non-linear sigma model field theory in the presence of a quantized topological theta-term. By studying lattice models of bosonic SPT states, we are able to identify, in their Euclidean path integral formulation, (discrete) Berry phases that hold relevant physical information on the nature of the SPT ground states. These discrete Berry phases are given intuitive physical interpretation in terms of instanton effects that capture the presence of a theta-term on the microscopic scale.