A range three elliptic deformation of the Hubbard model

TL;DR

This paper introduces a novel integrable deformation of the Hubbard model with a range 3 interaction that breaks spin and particle number conservation, and maps to a new nearest-neighbour integrable model.

Contribution

It presents the first non-trivial medium-range integrable deformation of the Hubbard model and explores its duality to a new nearest-neighbour model.

Findings

Deformation introduces a range 3 interaction term breaking spin and particle number conservation.

Mapped to a new integrable nearest-neighbour model via duality.

Computed R-matrices exhibit unusual elliptic spectral parameter dependence.

Abstract

In this paper we present a new integrable deformation of the Hubbard model. Our deformation gives rise to a range 3 interaction term in the Hamiltonian which does not preserve spin or particle number. This is the first non-trivial medium range deformation of the Hubbard model that is integrable. Our model can be mapped to a new integrable nearest-neighbour model via a duality transformation. The resulting nearest-neighbour model also breaks spin conservation. We compute the $R$-matrices for our models, and find that there is a very unusual dependence on the spectral parameters in terms of the elliptic amplitude.