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

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Beisert,  Niklas
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1002.1097
(Preprint), 609KB

JofPhysA_44_26_265202.pdf
(Any fulltext), 484KB

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Citation

Beisert, N. (2011). The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain. Journal of Physics A: Mathematical and General, 44(26): 265202. doi:10.1088/1751-8113/44/26/265202.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-6570-9
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.