On the partition function of the $Sp(4)$ integrable vertex model

TL;DR

This paper derives functional relations for an $Sp(4)$ symmetric integrable vertex model, enabling the calculation of its partition function per site and extending results to mixed representation models.

Contribution

It establishes new fusion relations and a transfer matrix inversion identity for the $Sp(4)$ vertex model, facilitating exact partition function computations.

Findings

Partition function per site for the fundamental $Sp(4)$ model computed.

Partition function per site for mixed four- and five-dimensional representations obtained.

Functional relations include a key transfer matrix inversion identity.

Abstract

In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental $Sp(4)$ representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the $Sp(4)$ symmetry.