On the ${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model

TL;DR

This paper investigates the boundary integrability of the ${ m U}_q[osp(1|2)]$ Temperley-Lieb model, deriving solutions for boundary conditions, eigenvalues, and Bethe ansatz equations to fully describe its spectrum.

Contribution

It constructs solutions to graded reflection equations and derives the complete spectrum of the model with diagonal boundaries using coordinate Bethe ansatz.

Findings

Derived boundary solutions for the model

Obtained eigenvalues and Bethe ansatz equations

Provided a full spectral description with diagonal boundaries

Abstract

This work concerns the boundary integrability of the ${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model. We constructed the solutions of the graded reflection equations in order to determine the boundary terms of the correspondig spin-1 Hamiltonian. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe ansatz. These equations provide the complete description of the spectrum of the model with diagonal integrable boundaries.