A Quantum Affine Algebra for the Deformed Hubbard Chain

Abstract

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above mentioned Yangian and to the conventional quantum affine sl(2|2) algebra in two special limits.

24 pages, v2: minor amendment of (7.2), v3: accepted for publication in JPA, minor corrections

References in corpus (8)

• Quantum Deformations of the One-Dimensional Hubbard Model
• On the Hopf algebra structure of the AdS/CFT S-matrix
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• The magnon kinematics of the AdS/CFT correspondence
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra

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