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

Giuseppe De Nittis; Santiago G. Rendel

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

Mathematical Physics 2026-07-01 v1 Operator Algebras

Authors: Giuseppe De Nittis , Santiago G. Rendel

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.

Keywords

topological phases Weyl C*-algebra pure state space homotopy classification K-theory topological insulators

Cite

@article{arxiv.2607.01183,
  title  = {A scheme for topological phases of the Weyl $C^*$-algebra},
  author = {Giuseppe De Nittis and Santiago G. Rendel},
  journal= {arXiv preprint arXiv:2607.01183},
  year   = {2026}
}

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29 pages