A note on homotopic versus isomorphic topological phases
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.