This paper proposes a generalization of the Kittel-Shore model to higher-rank quantum algebraic symmetries, including su(n), so(n), and exceptional Lie algebras. It presents a systematic framework for constructing higher-rank quantum deformations of long-range spin models, establishes algebraic Bethe ansatz solutions, and derives thermodynamic properties including phase transition behavior.
Key findings
The KS model can be generalized to higher-rank quantum algebraic symmetries.
A systematic framework for constructing higher-rank quantum deformations of long-range spin models is established.
Algebraic Bethe ansatz solutions for the generalized models are developed.
Thermodynamic properties and phase diagrams for su(3) and G2 cases are analyzed.
Limitations & open questions
The existing q-deformation is restricted to the su(2) case.
The generalization to su(n), so(n), and exceptional Lie algebras remains largely unexplored.