Integrable mixing of A_{n-1} type vertex models

SERGIO GRILLO; HUGO MONTANI

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2004 p. 2073 - 2089

0022-2488

Given a family of monodromy matrices T_0,T_1,...,T_{K-1} corresponding to integrable anisotropic vertex models of A_{n_{i}-1} type, i=0,1,...,K-1, we build up a related mixed vertex model by means of glueing the lattices on which they are defined, in such a way that integrability property is preserved. The glueing process is implemented through 1-dimensional representations of rectangular quantum matrix algebras A(R_{n_{i-1}}:R_{n_{i}}), namely, the glueing matrices M_{i}. Algebraic Bethe ansatz is applied on a pseudovacuum space with a selected basis and, for each element of this basis, it yields a set of nested Bethe ansatz equations matching up to the ones corresponding to an A_{m-1} quasi-periodic model, with m equal to min_{i in Z_{K}}{rankM_{i}}.