Recent results on integrable electronic models

TL;DR

This paper reviews methods for constructing and solving integrable electronic models, including extended Hubbard and constrained fermion models, highlighting new solvable cases and potential applications to spin systems.

Contribution

It introduces a unified approach using generalized permutator and Sutherland species techniques to generate and solve new classes of integrable electron Hamiltonians.

Findings

Constructed 56 new integrable electron models.

Solved the spectrum of a particular t-V model.

Identified connections to spin S models.

Abstract

We review the approach of generalized permutator to produce a class of integrable quantum Hamiltonians, as well as the technique of Sutherland species (SS) to map a subclass of it into solvable spinless fermions models. In particular, we apply the above scheme to construct integrable interacting electron Hamiltonians: first we review the extended Hubbard case, discussing both ground state and thermodynamics; then we pass to constrained fermion models, generating 56 integrable cases, among which both supersymmetric t-J model and infinite U Hubbard model are obtained, as well as other physically interesting cases, such as a particular t-V model. For the latter we describe how the complete spectrum can be gained by means of SS technique. Finally we speculate about possible applications to spin S models.