Quantum group deformation of the Kittel–Shore model

The Kittel--Shore (KS) Hamiltonian describes N spins with long-range interactions that are identically coupled, and therefore this (mean field) model is also known as the Heisenberg XXX model on the complete graph. In this paper, the underlying U(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 Uq(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 thermodynamical properties of the spin-$1/2$ q-KS model, the dependence of the Curie temperature in terms of the deformation parameter is studied through numerical analysis.