Quantum group deformation of the Kittel–Shore model

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="fraktur">su</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="fraktur">su</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> 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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> 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- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> -KS model, the dependence of the Curie temperature on the deformation parameter is studied through numerical analysis.