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Type: Journal article
Title: On the K-Theoretic Classification of Topological Phases of Matter
Author: Thiang, G.
Citation: Annales Henri Poincare, 2016; 17(4):757-794
Publisher: Springer
Issue Date: 2016
ISSN: 1424-0637
Statement of
Guo Chuan Thiang
Abstract: We present a rigorous and fully consistent K-theoretic framework for studying gapped phases of free fermions. It utilizes and profits from powerful techniques in operator K-theory, which from the point of view of symmetries such as time reversal, charge conjugation, and magnetic translations, is more general and natural than the topological version. In our model-independent approach, the dynamics are only constrained by the physical symmetries, which can be completely encoded using a suitable C*-superalgebra. Contrary to existing literature, we do not use K-theory groups to classify phases in an absolute sense, but to classify topological obstructions between phases. The Periodic Table of Kitaev is exhibited as a special case within our framework, and we prove that the phenomena of periodicity and dimension shifts are robust against disorder and magnetic fields.
Rights: © 2015 Springer Basel
DOI: 10.1007/s00023-015-0418-9
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