Field theory of symmetry-protected valence bond solid states in (2+1) dimensions

TL;DR

This paper develops a semiclassical field-theory framework using nonlinear sigma models with topological terms to distinguish symmetry-protected topological valence bond solid states in antiferromagnets across one to three dimensions.

Contribution

It introduces a novel field-theoretic approach that captures the topological features of SPT states and relates them to the behavior of strange correlators in higher dimensions.

Findings

Path integral distinguishes SPT from trivial states.

Topological terms influence the strange correlator behavior.

Two-dimensional strange correlator reduces to Haldane's spin correlator.

Abstract

This paper describes a semiclassical field-theory approach to the topological properties of spatially featureless Affleck-Kennedy-Lieb-Tasaki type valence bond solid ground states of antiferromagnets in spatial dimensions one to three. Using nonlinear sigma models set in the appropriate target manifold and augmented with topological terms, we argue that the path integral representation of the ground-state wave functional can correctly distinguish symmetry-protected topological ground states from topologically trivial ones. The symmetry-protection feature is demonstrated explicitly in terms of a dual field theory, where we take into account the nontrivial spatial structure of topological excitations, which are caused by competition among the relevant ordering tendencies. A temporal surface contribution to the action originating from the bulk topological term plays a central role in our study. We discuss how the same term governs the behavior of the so-called strange correlator. In particular, we find that the path integral expression for the strange correlator in two dimensions reduces to the well-known Haldane expression for the two point spin correlator of antiferromagnetic spin chains.