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arXiv:2603.27436

The Full Set of KMS-States for Abelian Kitaev Models

Danilo Polo Ojito, Emil V. Prodan

Published Mar 28, 2026• 0 citations
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Abstract

We first prove that the subalgebra $\mathcal{C}$ generated by the vertex and face operators of an abelian Kitaev model is a $C^\ast$-diagonal of the UHF algebra $\mathcal{A}$ of quasilocal observables. This gives us access to the Weyl groupoid $\mathcal{G}_\mathcal{C}$ associated with the $C^\ast$-inclusion $\mathcal{C} \hookrightarrow \mathcal{A}$, which supplies a valuable presentation of $\mathcal{A}$ as a groupoid $C^\ast$-algebra where the dynamics of the model are generated by a groupoid 1-cocycle $c_H$. Making appeal to the notion of $(c_H,β)$-KMS measures for this groupoid, we identify the full set of KMS states of the model and prove its uniqueness for $β\in [0,\infty)$. Furthermore, we show that its limit at $β\rightarrow \infty$ exists and coincides with the unique frustration-free ground state of the model.

DOI
10.48550/arxiv.2603.27436

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