Su(1,2) Algebraic Structure of the XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

TL;DR

This paper reveals that the XYZ antiferromagnetic model in the linear spin-wave frame possesses an su(1,2) algebraic structure, enabling algebraic diagonalization and providing insights into its energy spectrum.

Contribution

It explicitly demonstrates the su(1,2) algebraic structure of the XYZ antiferromagnetic model and develops an algebraic diagonalization method for solving its energy eigenvalues.

Findings

Energy eigenvalues obtained via algebraic transformations

Only one group solution is physically acceptable

Numerical solutions support the algebraic approach

Abstract

The $XYZ$ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an $su(1,2)$ algebraic structure: the Hamiltonian can be written as a linear function of the $su(1,2)$ algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.