The Full Set of KMS-States for Abelian Kitaev Models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917374462001152 |
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| author | Ojito, Danilo Polo Prodan, Emil |
| author_facet | Ojito, Danilo Polo Prodan, Emil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27436 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Full Set of KMS-States for Abelian Kitaev Models Ojito, Danilo Polo Prodan, Emil Mathematical Physics Strongly Correlated Electrons Operator Algebras Primary: 46L55, 82B10, Secondary: 37A55, 22A22, 46L05 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. |
| title | The Full Set of KMS-States for Abelian Kitaev Models |
| topic | Mathematical Physics Strongly Correlated Electrons Operator Algebras Primary: 46L55, 82B10, Secondary: 37A55, 22A22, 46L05 |
| url | https://arxiv.org/abs/2603.27436 |