The Full Set of KMS-States for Abelian Kitaev Models

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.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.

arXiv:2603.27436Mar 28, 20260 citations

Quantum Monte Carlo study of Kitaev models

譲治那須, Joji Nasu, 幸年求 +2 more

Feb 1, 20150 citations

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.