The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
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.
Cite
@article{arxiv.1002.1097,
title = {The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain},
author = {Niklas Beisert},
journal= {arXiv preprint arXiv:1002.1097},
year = {2011}
}
Comments
41 pages, v2: minor textual improvements, references added, v3: minor improvements, references added, change of convention x(v2)=h'x(v3)-ih