Algebra Solutions of Antiferromagnet-Antiferromagnet-Ferromagnet Quantum Heisenberg Chains Related to Sp(6,R) Lie Algebra

Abstract

Antiferromagnet-antiferromagnet-ferromagnet (AF-AF-F) quantum Heisenberg chains in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure, and its algebra solutions related to the Sp(6,R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(6,R)⊃U(1,2).