An Integrable Model with non-reducible three particle R-Matrix

TL;DR

This paper introduces a new integrable lattice model featuring non-reducible three-particle R-matrices, extending the conventional two-particle framework and solving the associated modified Yang-Baxter equations.

Contribution

It presents the first explicit construction of an integrable model with non-reducible three-particle R-matrices and derives the transfer matrix as an exponential of a non-local Hamiltonian.

Findings

Successfully solves modified Yang-Baxter equations for the model.

Derives the transfer matrix as a normal ordered exponential.

Establishes a new class of integrable models with multi-particle R-matrices.

Abstract

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved and an expression for the transfer matrix is found as a normal ordered exponential of a (non-local) Hamiltonian.