Eur. Phys. J. B 7, 627-633 (1999)
https://doi.org/10.1007/s100510050655

Multiplicity A_m models^*

Physics Department, University of Virginia, McCormick road, Charlottesville, VA 22901, USA

Received: 24 June 1998
Revised: 8 September 1998
Accepted: 10 September 1998
Published online: 15 February 1999

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.