The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain

TL;DR

This paper explores the classical limit of the quantum-deformed Hubbard model, deriving a new trigonometric classical r-matrix and analyzing its algebraic structure and symmetries.

Contribution

It introduces a novel classical trigonometric r-matrix for the quantum-deformed Hubbard chain and derives related Lie bialgebras, expanding understanding of its algebraic properties.

Findings

Derived a new classical trigonometric r-matrix

Established a one-parameter family of Lie bialgebras

Analyzed symmetries and limiting cases of the model

Abstract

The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum-deformation of the Hubbard model in the classical limit. This leads to a novel classical r-matrix of trigonometric kind. We derive the corresponding one-parameter family of Lie bialgebras as a deformation of the affine gl(2|2) Kac-Moody superalgebra. In particular, we discuss the affine extension as well as discrete symmetries, and we scan for simpler limiting cases, such as the rational r-matrix for the undeformed Hubbard model.