Symmetry Protected Topological phases of Quantum Matter

TL;DR

This paper reviews recent advances in understanding Symmetry Protected Topological (SPT) phases in quantum matter, emphasizing their physical properties, classifications, and implications for three-dimensional systems with symmetry.

Contribution

It provides a comprehensive overview of SPT phases, highlighting their physical characteristics, classifications, and significance in interacting quantum systems.

Findings

Classification of 3D SPT phases with realistic symmetries

Surface states protected by symmetry in SPT phases

Insights into the physical properties of SPT states

Abstract

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no exotic excitations but have non-trivial surface states that are protected by symmetry. We describe the various possible such phases and their properties in three dimensional systems with realistic symmetries. We develop many key ideas of the theory of these states using simple examples. The emphasis is on physical rather than mathematical properties. We survey insights obtained from the study of SPT phases for a number of other theoretical problems.