Quantum affine symmetry in vertex models

TL;DR

This paper explores higher spin generalizations of the six vertex model using quantum affine algebra symmetry, revealing that particles maintain spin 1/2 and the multi-particle space exhibits an RSOS-type structure, aligning with prior theories.

Contribution

It formulates the state space, transfer matrix, and operators of higher spin vertex models using representation theory, extending the understanding of their algebraic structure.

Findings

Particles have spin 1/2 regardless of representation level

Multi-particle space has an RSOS-type structure

Results agree with Reshetikhin's earlier proposals

Abstract

We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin $1/2$, and that the $n$-particle space has an RSOS-type structure rather than a simple tensor product of the $1$-particle space. This agrees with the picture proposed earlier by Reshetikhin.