Symmetry-Protected Topological Phases of Quantum Matter

TLDR

These states have a bulk gap and no exotic excitations but possess non‑trivial surface states protected by symmetry, similar to topological band insulators. The authors aim to describe recent progress and enumerate possible SPT phases, emphasizing physical properties and surveying insights for related theoretical problems. They develop the theory of SPT phases by generalizing topological band insulators to interacting systems and illustrating key concepts with simple examples.

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.