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The q-deformed SU-2 Heisenberg model in 3-dimensions

Zhong-Yi Lu, Yan Hong

Published Jul 1, 1991• 0 citations
OpenAlex

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Abstract 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 ( 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 ( 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.

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Following the deformed boson scheme leading to the su(1,1)-algebra, a certain simple boson system is deformed in the framework of the second Holstein-Primakoff representation. With the aid of the MYT boson mapping, the second representation arrives at the first Holstein-Primakoff representation. The su(1,1)-algebraic model obtained in this procedure is compared with that in the Schwinger representation investigated by three of the present authors (A.K., Y.T. and M.Y.).

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Two-dimensional Heisenberg model with weak anisotropy

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Abstract 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 ( 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 ( 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.