Quantum inverse method for two-dimensional ice and ferroelectric lattice models

The quantum inverse scattering transform method previously developed for continuum field theories is applied to the exactly soluble symmetric six-vertex (ice or ferroelectric) lattice model. Operators analogous to those which appear in the quantum inverse treatment of the nonlinear Schrödinger and sine–Gordon equations are constructed on the lattice by forming strings of vertices contracted over horizontal arrows. From the commutation relations for these operators, exact formulas for the eigenstates and eigenvalues of the transfer matrix are obtained without making an explicit ansatz for the wave functions. These results illustrate the connection between the quantum inverse method and the transfer matrix formalism for lattice models.