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https://hdl.handle.net/2440/101043
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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 1793-6977 |
Statement of Responsibility: | 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 |
Grant ID: | http://purl.org/au-research/grants/arc/DP110100072 |
Published version: | http://dx.doi.org/10.1142/s021988781550098x |
Appears in Collections: | Aurora harvest 3 Mathematical Sciences publications |
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