The Yangian Symmetry of the Hubbard Models with Variable Range Hopping

TL;DR

This paper uncovers two pairs of Yangian symmetries for generalized Hubbard models with variable-range hopping, extending known symmetries to more complex models and revealing their mutual commutativity and dynamical origin.

Contribution

It introduces new Yangian symmetries for trigonometric and hyperbolic Hubbard models with non-nearest-neighbour hopping, generalizing previous symmetry structures.

Findings

Yangian symmetries are mutually commuting.

Symmetries include known cases as limits.

Symmetries have a dynamical origin.

Abstract

We present two pairs of Y($sl_2$) Yangian symmetries for the trigonometric and hyperbolic versions of the Hubbard model with non-nearest-neighbour hopping. In both cases the Yangians are mutually commuting, hence can be combined into a Y($sl_2$)$\oplus$Y($sl_2$) Yangian. Their mutual commutativity is of dynamical origin. The known Yangians of the Haldane-Shastry spin chain and the nearest neighbour Hubbard model are contained as limiting cases of our new representations.