Quantum Group Approach to a soluble vertex model with generalized ice-rule

TL;DR

This paper introduces and solves a new quantum group-based vertex model with a generalized ice-rule, revealing a free-fermion limit and potential links to lattice neutral plasma via algebraic structures.

Contribution

It constructs and analytically solves a novel vertex model using quantum group representations, extending the ice-rule concept and exploring its algebraic and physical properties.

Findings

Existence of a free-fermion limit with rich operator structure

Detailed study of the generalized ice-rule properties

Potential connection to lattice neutral plasma through algebraic structures

Abstract

Using the representation of the quantum group $SL_q$(2) by the Weyl ope\-ra\-tors of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertices is subjected to a genera\-li\-zed form of the so-called ``ice-rule'', its property are studied in details and its free energy calculated with the method of quantum inverse scattering. Remarkably in analogy with the usual six-vertex model, there exists a ``Free-Fermion'' limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the Fermion-Boson correspondence.