Quasi-classical descendants of disordered vertex models with boundaries

Antonio Di Lorenzo; Luigi Amico; Kazuhiro Hikami; Andreas Osterloh; Gaetano Giaquinta

doi:10.1016/s0550-3213(02)00811-8

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Quasi-classical descendants of disordered vertex models with boundaries

Antonio Di Lorenzo·Luigi Amico·Kazuhiro Hikami·Andreas Osterloh·Gaetano Giaquinta

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Abstract

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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Antonio Di Lorenzo, Luigi Amico, Kazuhiro Hikami, Andreas Osterloh, Gaetano Giaquinta. 2002-10-24. Quasi-classical descendants of disordered vertex models with boundaries. https://doi.org/10.1016/s0550-3213(02)00811-8

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