Exact Solution of a Vertex Model with Unlimited Number of States Per Bond

TL;DR

This paper provides an exact solution for a 2D vertex model with infinitely many bond states, linking it to quantum spin chains and analyzing its ground-state correlations via conformal field theory.

Contribution

It introduces an exact solution for a vertex model with unlimited bond states and connects it to quantum spin chains using conformal field theory predictions.

Findings

Eigenvalues and eigenvectors of the transfer matrix are obtained.

Long-distance behavior of ground-state correlations is derived.

Model is a classical analogue of a quantum spin chain with unlimited spin.

Abstract

The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain with an unlimited value of spin. This quantum chain is studied using general predictions of conformal field theory. The long-distance behaviour of some ground-state correlation functions is derived from a finite-size analysis of the gapless excitations.