Exactly Solvable Interacting Spin-Ice Vertex Model

TL;DR

This paper introduces a new exactly solvable five-vertex model with diagonal interactions, extending the six-vertex model, and applies the matrix product ansatz to analyze its phase diagram and critical behavior.

Contribution

It presents the first application of the matrix product ansatz to a new class of exactly solvable vertex models with diagonal interactions.

Findings

Model exhibits massless phases with conformal field theory characteristics

Phase diagram and free energy are analytically and numerically determined

Critical exponents vary continuously with parameters

Abstract

A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of models includes in a special limit the standard six-vertex model. 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. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases and our analyticaland numerical analysis indicate that such phases are governed by a conformal field theory with central charge $c=1$ and continuosly varying critical exponents.