Fusion of the $q$-Vertex Operators and its Application to Solvable Vertex Models

TL;DR

This paper introduces new q-vertex operators derived from fusion procedures to diagonalize transfer matrices of inhomogeneous 6-vertex models, revealing their particle structure and ground state degeneracies.

Contribution

It constructs novel q-vertex operators from level one operators via fusion, providing a new algebraic approach to analyze vertex models in the anti-ferroelectric regime.

Findings

Diagonalization of transfer matrices using new q-vertex operators

Description of ground state degeneracies through crystal isomorphisms

Simplified representation-theoretic understanding of particle structures

Abstract

We diagonalize the transfer matrix of the inhomogeneous vertex models of the 6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex operators. The special cases of those models were used to diagonalize the s-d exchange model\cite{W,A,FW1}. New vertex operators are constructed from the level one vertex operators by the fusion procedure and have the description by bosons. In order to clarify the particle structure we estabish new isomorphisms of crystals. The results are very simple and figure out representation theoretically the ground state degenerations.