Quantum group deformation of the Kittel--Shore model

• URL: http://arxiv.org/abs/2502.20884v1
• Date: Fri, 28 Feb 2025 09:31:53 GMT
• Title: Quantum group deformation of the Kittel--Shore model
• Authors: A. Ballesteros, I. Gutiérrez-Sagredo, V. Mariscal, J. J. Relancio,
• Abstract summary: The Kittel--Shore (KS) Hamiltonian describes $N$ spins with long-range interactions that are identically coupled.<n>In this paper, the underlying $mathfraksu(2)$ coalgebra symmetry of the KS model is demonstrated for arbitrary spins.<n>The quantum deformation of the KS Hamiltonian ($q$-KS model) is obtained using the corresponding $mathfraksu_q(2)$ quantum group.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Kittel--Shore (KS) Hamiltonian describes $N$ spins with long-range interactions that are identically coupled. In this paper, the underlying $\mathfrak{su}(2)$ 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 $\mathfrak{su}_q(2)$ 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 in both ferromagnetic and antiferromagnetic couplings, and the cases with $N=2,3,$ and $4$ spins are studied in detail. The higher-spin $q$-KS models are sketched.

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