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.

41 pages, v2: minor textual improvements, references added, v3: minor improvements, references added, change of convention x(v2)=h'x(v3)-ih

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Cited by in corpus (2)

• Yangians, S-matrices and AdS/CFT
• On the perturbative S-matrix of generalized sine-Gordon models