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A short guide to topological terms in the effective theories of condensed matter
Akihiro Tanaka1, Shintaro Takayoshi1
1Computational Materials Science Unit, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan.
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 a generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.
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According to its composition, the matter can be classified into two broad categories — pure substances and mixtures.
A pure substance is a form of matter that has a constant composition throughout with uniform properties. For example, any sample of sucrose has the same composition and same physical properties, such as melting point, color, and sweetness, regardless of the source from which it is isolated.
A mixture is composed of two or...

