Generalized Yang-Baxter Equation

TL;DR

This paper introduces a generalized Yang-Baxter equation that allows for the construction of integrable 2D lattice models with commuting two-layer transfer matrices, expanding the scope of integrable systems.

Contribution

It proposes a new generalized form of the Yang-Baxter equation and provides explicit solutions linked to the $sl(3)$ chiral Potts model.

Findings

Explicit solutions to the generalized equations are found.

The generalized equations enable two-layer transfer matrices to commute.

Connections are established with the $sl(3)$ chiral Potts model.

Abstract

A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Botzmann weights of the $sl(3)$ chiral Potts model.