A note on the boundary spin $s$ XXZ chain

TL;DR

This paper investigates the boundary spin s XXZ chain using algebraic Bethe ansatz, deriving reference states through difference equations and identifying the spectrum for general anisotropy parameters.

Contribution

It introduces a method to construct reference states for the boundary spin s XXZ model using difference equations and q-hypergeometric series, advancing the algebraic Bethe ansatz approach.

Findings

Derived reference states involving q-hypergeometric series.

Constructed Bethe states for the boundary spin s XXZ model.

Identified the spectrum for generic anisotropy values.

Abstract

The open spin $s$ XXZ model with non-diagonal boundaries is considered. Within the algebraic Bethe ansatz framework and in the spirit of earlier works we derive suitable reference states. The derivation of the reference state is the crucial point in this investigation, and it involves the solution of sets of difference equations. For the spin $s$ representation, expressed in terms of difference operators, the pseudo-vacuum is identified in terms of $q$-hypergeometric series. Having specified such states we then build the Bethe states and also identify the spectrum of the model for generic values of the anisotropy parameter $q$.