# A quantum affine algebra for the deformed Hubbard chain

@article{Beisert2012AQA,
title={A quantum affine algebra for the deformed Hubbard chain},
author={Niklas Beisert and Wellington Gall{\'e}as and Takuya Matsumoto},
journal={Journal of Physics A},
year={2012},
volume={45},
pages={365206}
}
• Published 2012
• Mathematics, Physics
• Journal of Physics A
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended 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 algebra in two… Expand
61 Citations

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#### References

SHOWING 1-10 OF 67 REFERENCES
The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
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 theExpand
Quantum Deformations of the One-Dimensional Hubbard Model
• Physics, Mathematics
• 2008
The centrally extended superalgebra psu(2|2) �R 3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. HereExpand
The Classical r-Matrix of AdS/CFT and its Lie Bialgebra Structure
• Mathematics, Physics
• 2009
In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) $${\mathfrak{u}(2|2)}$$ symmetry,Expand
Exact integrability of the one-dimensional Hubbard model.
• Shastry
• Physics, Medicine
• Physical review letters
• 1986
It is shown in this work that any two transfer matrices of a family commute mutually, at the root of the commutation relation is the ubiquitous Yang-Baxter factorization condition. Expand
Hopf algebra structure of the AdS/CFT S-matrix
• Physics
• 2006
We formulate the Hopf algebra underlying the su(2/2) world sheet S-matrix of the AdS{sub 5}xS{sup 5} string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1/2)Expand
The magnon kinematics of the AdS/CFT correspondence
• Physics
• 2006
The planar dilatation operator of N = 4 supersymmetric Yang-Mills is the hamiltonian of an integrable spin chain whose length is allowed to fluctuate. We will identify the dynamics of lengthExpand
Planar N = 4 gauge theory and the Hubbard model
• Physics
• 2005
Recently it was established that a certain integrable long-range spin chain describes the dilatation operator of N = 4 gauge theory in the su(2) sector to at least three-loop order, while exhibitingExpand
Q-deformed su(2|2) boundary S-matrices via the ZF algebra
• Physics
• 2008
Beisert and Koroteev have recently found a bulk S-matrix corresponding to a q-deformation of the centrally-extended su(2|2) algebra of AdS/CFT. We formulate the associated Zamolodchikov-FaddeevExpand
A secret symmetry of the AdS/CFT S-matrix
• Physics
• 2007
We find a new quantum Yangian symmetry of the AdS/CFT S-matrix, which complements the original (2|2) symmetry to (2|2) and does not have a Lie algebra analog. Our finding is motivated by the YangianExpand
Review of AdS/CFT Integrability. Chapter VI.2: Yangian Algebra
We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the $${\mathcal{N} = 4}$$Expand