Quasi-classical descendants of disordered vertex models with boundaries

TL;DR

This paper derives a new class of integrable long-range $su(2)$-spin chains with boundary conditions, using quasi-classical expansions of vertex models, and analyzes their spectrum and fermionic representations.

Contribution

It introduces a one-parameter extension of integrable $su(2)$-spin chains with boundary reflections derived from quasi-classical vertex models.

Findings

Exact spectrum obtained via algebraic Bethe ansatz.

Models describe confined fermions with pairing interactions.

Extensions to $su(n)$-spin chains are discussed.

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.