Symmetry Protected Topological phases and Generalized Cohomology

TL;DR

This paper explores the classification of symmetry-protected topological (SPT) phases using generalized cohomology theories, proposing a concrete spectrum description and comparing it with existing models.

Contribution

It introduces a new concrete description of the spectrum underlying SPT classification and advances the theoretical framework connecting SPT phases with generalized cohomology.

Findings

Proposes a concrete spectrum for classifying SPT phases.

Provides a comparison with existing classification methods.

Enhances the theoretical understanding of SPT phase classification.

Abstract

We discuss the classification of SPT phases in condensed matter systems. We review Kitaev's argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing constructions in the literature.