Combinatorial point for higher spin loop models

TL;DR

This paper investigates integrable higher spin loop models at a specific quantum parameter point, deriving ground state properties and sum rules through inhomogeneities, advancing understanding of their mathematical structure.

Contribution

It introduces a new analysis of higher spin loop models at a special point, providing explicit ground state eigenvalues, eigenvectors, and sum rules.

Findings

Explicit ground state eigenvalues and eigenvectors derived.

Sum rule for ground state entries established.

Enhanced understanding of higher spin loop models at special quantum points.

Abstract

Integrable loop models associated with higher representations (spin k/2) of U_q(sl(2)) are investigated at the point q=-e^{i\pi/(k+2)}. The ground state eigenvalue and eigenvectors are described. Introducing inhomogeneities into the models allows to derive a sum rule for the ground state entries.