A scheme for topological phases of the Weyl $C^*$-algebra

Summary · qwen2.5:32b

The article presents a classification scheme for topological phases of matter using the topology of pure states in a model $C^*$-algebra, where phases are characterized by homotopy classes of state sections. This scheme generalizes the $K$-theoretic classification of gapped spectral projectors for A and AI type topological insulators when applied to translation-invariant Weyl $C^*$-algebra states.

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Excerpt

arXiv:2607.01183v2 Announce Type: replace Abstract: In this work, we introduce a classification scheme for topological phases of matter based on the topology of the space of pure states of a model $C^*$-algebra. Under it, topological phases are described by homotopy classes of sections of certain fiber bundles of (pure) states. Applying this classification procedure on states of the Weyl $C^*$-algebra that are invariant under translations by a lattice, we recover the $K$-theoretic classification of gapped spectral projectors for topological insulators of types A and AI, thus essentially generalizing this notion.