Global anomaly detection in two-dimensional symmetry-protected topological phases

TL;DR

This paper investigates the edge anomalies of 2D bosonic symmetry-protected topological phases, linking them to cohomology classifications and demonstrating detection methods via tensor network simulations.

Contribution

It provides a detailed analysis of edge anomalies in 2D SPT phases, connecting physical interpretations to cohomology and proposing numerical detection schemes.

Findings

Edge anomalies relate to obstructions in orbifolding.

Cohomology classification describes SPT phases.

Tensor network methods can detect symmetry-protected order.

Abstract

Edge theories of symmetry-protected topological phases are well-known to possess global symmetry anomalies. In this work we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyse the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.