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

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.

18 pages, 6 figures, Pedagogical review article written for the focus issue "Materials Science of Topological Insulators and Superconductors" of the journal, Science and Technology of Advanced Materials (STAM)

References in corpus (1)

• Geometric phases and the magnetization process in quantum antiferromagnets

Cited by in corpus (4)

• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Topological effect on the Anderson transition in chiral symmetry classes
• Quantum kinetic theory of flux-carrying Brownian particles
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors