A short guide to topological terms in the effective theories of condensed matter

TL;DR

This paper provides an accessible overview of topological terms in effective theories of condensed matter, illustrating their role in quantum magnetism, superfluids, and symmetry-protected topological phases.

Contribution

It offers a clear introduction to topological terms and their applications across various condensed matter systems, including recent developments in topological phases.

Findings

Topological terms are crucial in describing quantum effects in condensed matter.

Examples include quantum magnetism, superfluids, and superconductors.

Recent extensions to symmetry-protected topological phases.

Abstract

This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors. We then briefly discuss how these ideas are now finding incarnations in the studies of symmetry-protected topological phases, which are in a sense the generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.