Quantum deformations of the one-dimensional Hubbard model

doi:10.1088/1751-8113/41/25/255204

Quantum deformations of the one-dimensional Hubbard model

Niklas Beisert et al 2008 J. Phys. A: Math. Theor. 41 255204 (47pp) doi: 10.1088/1751-8113/41/25/255204

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Niklas Beisert¹ and Peter Koroteev^1,2,3
¹ Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany
² Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, Moscow 117259, Russia
³ Institute for Nuclear Research, Prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia
E-mail: nbeisert@aei.mpg.de and koroteev@aei.mpg.de

Abstract. The centrally extended superalgebra $\alg{psu}(2|2) \ltimes{\bb R}^3$ was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation ${\rm U}_q(\alg{psu}(2|2) \ltimes{\bb R}^3)$ and derive the fundamental R-matrix. From the latter we deduce an integrable spin-chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.

PACS numbers: 02.30.Ik, 02.20.Uw, 75.10.Pq

Print publication: Issue 25 (27 June 2008)
Received 3 April 2008
Published 28 May 2008

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Quantum deformations of the one-dimensional Hubbard model

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