Quantum group deformation of the Kittel--Shore model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912798724849664 |
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| author | Ballesteros, A. Gutiérrez-Sagredo, I. Mariscal, V. Relancio, J. J. |
| author_facet | Ballesteros, A. Gutiérrez-Sagredo, I. Mariscal, V. Relancio, J. J. |
| contents | The Kittel--Shore (KS) Hamiltonian describes $N$ spins with long-range interactions that are identically coupled; therefore, this (mean-field) model is also known as the Heisenberg XXX model on the complete graph. In this paper, the underlying $U(\mathfrak{su}(2))$ coalgebra symmetry of the KS model is demonstrated for arbitrary spins, and the quantum deformation of the KS Hamiltonian ($q$-KS model) is obtained using the corresponding $U_q(\mathfrak{su}(2))$ quantum group. By construction, the existence of such a symmetry guarantees that all integrability properties of the KS model are preserved under $q$-deformation. In particular, the $q$-KS model for spin-$1/2$ particles is analysed, the cases with $N=2$ and $3$ spins are studied in detail, and higher-spin $q$-KS models are sketched. As a first excursion into the thermodynamic properties of the spin-$1/2$ $q$-KS model, the dependence of the Curie temperature on the deformation parameter is studied through numerical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum group deformation of the Kittel--Shore model Ballesteros, A. Gutiérrez-Sagredo, I. Mariscal, V. Relancio, J. J. Mathematical Physics Quantum Physics The Kittel--Shore (KS) Hamiltonian describes $N$ spins with long-range interactions that are identically coupled; therefore, this (mean-field) model is also known as the Heisenberg XXX model on the complete graph. In this paper, the underlying $U(\mathfrak{su}(2))$ coalgebra symmetry of the KS model is demonstrated for arbitrary spins, and the quantum deformation of the KS Hamiltonian ($q$-KS model) is obtained using the corresponding $U_q(\mathfrak{su}(2))$ quantum group. By construction, the existence of such a symmetry guarantees that all integrability properties of the KS model are preserved under $q$-deformation. In particular, the $q$-KS model for spin-$1/2$ particles is analysed, the cases with $N=2$ and $3$ spins are studied in detail, and higher-spin $q$-KS models are sketched. As a first excursion into the thermodynamic properties of the spin-$1/2$ $q$-KS model, the dependence of the Curie temperature on the deformation parameter is studied through numerical analysis. |
| title | Quantum group deformation of the Kittel--Shore model |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2502.20884 |