On the C*-algebraic approach to topological phases for insulators

الأصل · EN

The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological space to which the Hamiltonians belong. We advocate that this space should be the C*-algebra of observables. We relate the symmetries of insulators to graded real structures on the observable algebra and classify the topological phases using van Daele's formulation of K-theory. This is related but not identical to Thiang's recent approach to classify topological phases by K-groups in Karoubi's formulation.