Exact solution of the lattice vertex model analog of the coupled Bariev XY chains

TL;DR

This paper provides an exact algebraic Bethe Ansatz solution for a lattice vertex model that is an analog of coupled Bariev XY chains, including explicit eigenvalues of the transfer matrix.

Contribution

It introduces a novel algebraic Bethe Ansatz solution for a specific vertex model related to Bariev XY chains, incorporating Hecke symmetry.

Findings

Explicit eigenvalues of the transfer matrix are derived.

The commutation rules involve Hecke symmetry.

The solution advances understanding of integrable models related to XY chains.

Abstract

We present the algebraic Bethe Ansatz solution for the vertex model recently proposed by Zhou as the classical analog of the Bariev interacting XY chains. The relevant commutation rules between the creation fields contain the Hecke symmetry pointed out recently by Hikami and Murakami. The eigenvalues of the corresponding transfer matrix are explicitly given.