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arXiv:1412.4191 [math-ph]AbstractReferencesReviewsResources

A note on homotopic versus isomorphic topological phases

Guo Chuan Thiang

Published 2014-12-13Version 1

Two gapped Hamiltonians compatible with given symmetry constraints may be isomorphic, but not homotopic to each other. We illustrate this with a simple model for Class AIII insulators in one spatial dimension, where a winding number measures the failure of homotopy between the gapped Hamiltonians for two insulators. This suggests that the notion of phases, up to homotopy, should be a relative one rather than an absolute one. We also analyse these issues in the context of K-theory.

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