A matrix product ansatz solution of an exactly solvable interacting vertex model

A special family of solvable five-vertex model is introduced on a square lattice. Beyond the usual nearest neighbor interactions, the vertices defining the model also interact along one of the diagonals of the lattice. This family of models includes on a special limit the standard six-vertex model (1,2). The exact solution of these models gives the first application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains.