Integrable Extended Hubbard Hamiltonians from Symmetric Group Solutions

TL;DR

This paper classifies all 1D integrable extended Hubbard models derived from symmetric group solutions of the Yang-Baxter equation, revealing 96 such models linked to generalized permutators.

Contribution

It identifies all integrable extended Hubbard Hamiltonians from symmetric group solutions, expanding the understanding of their algebraic structure and providing new models including known ones.

Findings

96 integrable models identified

Models linked to symmetric group generalized permutators

Includes known models like EKS

Abstract

We consider the most general form of extended Hubbard Hamiltonian conserving the total spin and number of electrons, and find all the 1-dimensional completely integrable models which can be derived from first degree polynomial solution of the Yang-Baxter equation. It is shown that such models are 96. They are identified with the 16-dimensional representation of a new class of solutions of symmetric group relations, acting as generalized permutators. As particular examples, the EKS and some other known models are obtained.