Crystalizing the Spinon Basis

TL;DR

This paper introduces a new crystal basis description for higher spin XXZ models, revealing fermionic character formulas and Yangian structures, and proposes conjectural formulas for multi quasi-particle states at q=0.

Contribution

It provides a novel crystal basis framework for higher spin XXZ models using creation operators at q=0, linking to fermionic formulas and Yangian structures.

Findings

New crystal basis description for higher spin XXZ models.

Derived fermionic character formulas and Yangian structures.

Proposed conjectural formulas for multi quasi-particle states at q=0.

Abstract

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level $k$ integrable highest weight $U_q(\widehat{sl_2})$ modules in terms of the creation operators at $q=0$ (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also derived the conjectural formulas for the multi quasi-particle states at $q=0$.