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Type: Journal article
Title: Topological phases: isomorphism, homotopy and K-theory
Author: Thiang, G.
Citation: International Journal of Geometric Methods in Modern Physics, 2015; 12(9):1550098-1-1550098-14
Publisher: World Scientific
Issue Date: 2015
ISSN: 0219-8878
Statement of
Guo Chuan Thiang
Abstract: Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modeled by vector bundles over Brillouin tori, physically relevant equivalences include isomorphism, homotopy, and K-theory, which are inequivalent but closely related. We discuss an important subtlety which arises in the chiral Class AIII systems, where the winding number invariant is shown to be relative rather than absolute as is usually assumed. These issues are then analyzed and reconciled in the language of K-theory.
Keywords: Topological phases; homotopy theory; K-theory; C∗ -algebras
Rights: © World Scientific Publishing Company
DOI: 10.1142/S021988781550098X
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Mathematical Sciences publications

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