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

Understand

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.