From Topological Quantum Field Theory to Topological Materials

This chapter presents a review of many of the ideas of topology as they arise out of, and are applied to, physical systems. It introduces some of the more theoretical and mathematical aspects of topological quantum field theory (TQFT). The Chern–Simons theory gives an explicit example of a TQFT on a space with no boundary. Many TQFTs have connections to a somewhat different type of quantum field theory called conformal field theory (CFT). The chapter focuses on trivalent kitaev spin lattice models because they not only serve as further, and more transparent, examples of TQFTs, but they provide important insights into the microscopic details of topological phases while abstracting themselves from irrelevant physical complications. It explains the relevance of the theoretical results both to test the theory's predictions and to open the way for new research.