The Yangian symmetry of the Hubbard Model

TL;DR

This paper reveals that the one-dimensional Hubbard model possesses a hidden infinite-dimensional Yangian symmetry, extending its known algebraic structure and deepening understanding of its integrability properties.

Contribution

The authors identify a new Yangian symmetry structure in the Hubbard model, showing it as a direct sum of two $sl(2)$-Yangians, which extends the known $sl(2) imes sl(2)$ symmetry.

Findings

Hubbard model has an infinite-dimensional algebra of symmetries.

The symmetry is a direct sum of two $sl(2)$-Yangians.

Yangian deformation parameters relate to the model's coupling constant.

Abstract

We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two $ sl(2) $-Yangians. This $ Y(sl(2)) \oplus Y(sl(2)) $ symmetry is an extension of the well-known $ sl(2) \oplus sl(2) $ . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.