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

Using the representation of the quantum group SLq(2) by the Weyl operators 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 generalized 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. e-mail: [email protected] e-mail: [email protected]