Multiplicity A_m Models

TL;DR

This paper introduces new integrable models based on A_m Lie algebras, extending previous su(2) XX spin-chain models, and demonstrates their integrability using the quantum inverse scattering method and algebraic Bethe Ansatz.

Contribution

It generalizes the construction of XXC models to A_m Lie algebra chains and establishes their integrability and algebraic structure.

Findings

Derived R-matrix representing the Hecke algebra

Proved integrability via quantum inverse scattering method

Diagonalized transfer matrices using algebraic Bethe Ansatz

Abstract

Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes.