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 (28)

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• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On deformations of AdS_n x S^n supercosets
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• Integrability of the AdS_5 x S^5 superstring and its deformations
• The Quantum Deformed Mirror TBA I
• The spectral problem for strings on twisted AdS_5 x S^5
• Yangians, S-matrices and AdS/CFT
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• A Relativistic Relative of the Magnon S-Matrix
• Non-split and split deformations of AdS_5
• On the perturbative S-matrix of generalized sine-Gordon models
• The Bound State S-matrix of the Deformed Hubbard Chain
• Integrable strings for AdS/CFT
• Maximally extended sl(2|2) as a quantum double
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Pohlmeyer reduction for superstrings in AdS space
• The Quantum Affine Origin of the AdS/CFT Secret Symmetry
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)
• Quantum deformation of cubic string field theory
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries