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

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

2010-02-05

arxiv.org/abs/1002.1097v3

J.Phys.A44:265202,2011

Physics

Mathematical Physics

41 pages, v2: minor textual improvements, references added, v3: minor improvements, references added, change of convention x(v

Scientific paper

10.1088/1751-8113/44/26/265202

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.

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