Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/109379
Type: | Conference paper |
Title: | On the K-Theoretic classification of topological phases of matter |
Author: | Thiang, G. |
Citation: | Proceedings of Science, 2014, vol.15-18-July-2014, pp.1-6 |
Publisher: | SISSA |
Publisher Place: | Online |
Issue Date: | 2014 |
ISSN: | 1824-8039 |
Conference Name: | 14th Annual International Symposium on Frontiers of Fundamental Physics (FFP14) (15 Jul 2014 - 18 Jul 2014 : Marseille, France) |
Statement of Responsibility: | Guo Chuan Thiang |
Abstract: | A K-theoretic approach to the study of gapped topological phases was suggested by Kitaev, who produced a Periodic Table of topological insulators and superconductors, modelled on Bott periodicity. We take the algebraic viewpoint, and study gapped phases of free fermions through a twisted crossed product C*-superalgebra associated to the symmetry data of the dynamics. We identify the K-theoretic difference-group of this symmetry algebra, in the sense of Karoubi, as the appropriate point of entry for K-theory. Thus, K-theory provides groups of obstructions between symmetry-compatible gapped Hamiltonians, rather than classification groups for the Hamiltonians themselves. The phenomena of periodicity and dimension-shifts in the difference-groups is shown to be a robust consequence of various isomorphisms in operator K-theory, which have no commutative counterpart. |
Description: | Frontiers of Fundamental Physics : session Mathematical Physics |
Rights: | Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. |
Published version: | https://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=224 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_109379.pdf | Published version | 212.8 kB | Adobe PDF | View/Open |
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