Abstract
AbstractWe consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants inKO*(Ar)withAaC*,r-algebra of allowed deformations. WhenA=C*(X), the Roe algebra of a coarse spaceX, and we restrict to gapped ground states that are locally equivalent with respectX, aK-homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance ofK-homology to free-fermionic SPT phases.
Funder
Japan Society for the Promotion of Science
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
3 articles.
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