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Title: Topological phases of matter, symmetries, and K-theory
Author: Thiang, Guo Chuan
ISNI:       0000 0004 5369 5256
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2014
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This thesis contains a study of topological phases of matter, with a strong emphasis on symmetry as a unifying theme. We take the point of view that the "topology" in many examples of what is loosely termed "topological matter", has its origin in the symmetry data of the system in question. From the fundamental work of Wigner, we know that topology resides not only in the group of symmetries, but also in the cohomological data of projective unitary-antiunitary representations. Furthermore, recent ideas from condensed matter physics highlight the fundamental role of charge-conjugation symmetry. With these as physical motivation, we propose to study the topological features of gapped phases of free fermions through a Z2-graded C*-algebra encoding the symmetry data of their dynamics. In particular, each combination of time reversal and charge conjugation symmetries can be associated with a Clifford algebra. K-theory is intimately related to topology, representation theory, Clifford algebras, and Z2-gradings, so it presents itself as a powerful tool for studying gapped topological phases. Our basic strategy is to use various K
Supervisor: Hannabuss, Keith Sponsor: Clarendon Fund
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Quantum theory (mathematics) ; Theoretical physics ; Algebraic topology ; Topological matter ; K-theory