Quasi-classical descendants of disordered vertex models with boundaries

Details Quasi-classical descendants of disordered vertex models with boundaries Quasi-classical descendants of disordered vertex models with boundaries

2002-06-26

arxiv.org/abs/cond-mat/0206521v2

Nucl.Phys. B644 (2002) 409-432

Physics

Condensed Matter

Statistical Mechanics

27 pages; 2 eps figures; elsart. Revised version, appendix C added

Scientific paper

10.1016/S0550-3213(02)00811-8

We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or reflection equation). As final product, integrable $su(2)$-spin chains interacting with a long range with $XXZ$ anisotropy are obtained. The spin-spin couplings are non uniform, and a non uniform tunable external magnetic field is applied; the latter can be obtained when the boundary conditions are assumed to be quasi-classical as well. The exact spectrum is achieved by algebraic Bethe ansatz. Having realized the $su(2)$ operators in terms of fermions, the class of models we found turns out to describe confined fermions with pairing force interactions. The class of models presented in this paper is a one-parameter extension of certain Hamiltonians constructed previously. Extensions to $su(n)$-spin open chains are discussed.

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