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

Johannes Kellendonk

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arXiv · 1509.06271

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

Johannes Kellendonk

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Abstract

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.

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BibTeX RIS

Johannes Kellendonk. 2017-02-17. On the C*-algebraic approach to topological phases for insulators. https://arxiv.org/abs/1509.06271

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