An index for two-dimensional SPT states

TL;DR

This paper introduces a new index for classifying two-dimensional symmetry-protected topological (SPT) states in bosonic lattice systems, providing a tool to distinguish different SPT phases.

Contribution

The paper defines a novel index for 2D G-invariant invertible states, establishing it as an invariant for SPT phase classification.

Findings

The index is well-defined in the thermodynamic limit.

The index remains invariant under SPT phase transformations.

It offers a new method for classifying 2D bosonic SPT states.

Abstract

We define an index for 2d $G$-invariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group $G$. We show that this index is an invariant of SPT phase.