Quantum deformations of the one-dimensional Hubbard model

By N. Beisert, P. Koroteev. Journal of Physics A: Mathematical and Theoretical, 2008

162 citations recorded by the source corpus.

The centrally extended superalgebra 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 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/781fbad6b51cc265a5a4f1dd27a7506b8a3ec496

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Integrable deformations of strings on symmetric spaces (2014, background): “The S-matrix of the deformed theory is built on the R-matrix of the quantum group written down in [5] and can be shown to satisfy all the axioms of S-matrix theory as long as either q is real and arbitrary or q = eiπ/k for an integer k [6, 7].”
On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, methodology): “Infact, the tree-level bosonic S-matrix was also computed and quite successfully matched with the semi-classical limit of the q-deformed S-matrix computed in [18, 19].”
The complete worldsheet S matrix of superstrings on AdS3×S3×T4 with mixed three-form flux (2014, background): “It is likely that this parameter space can be further enhanced by the study of so-called η-deformations [67–71].”
Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence (2014, result): “It would be an important task to compare the results with the deformed S-matrices [40–47].”
S-matrix for strings on η-deformed AdS5 × S5 (2013, background): “It appears that this centrally extended psu(2|2), or more precisely its universal enveloping algebra, admits a natural deformation psuq(2|2) in the sense of quantum groups [6, 7].”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “This road has been taken in the case of AdS5/CFT4, where a plethora of deformations has been shows to preserve integrability, such as orbifolds [247,248] and T-duality-shift-T-duality (TsT) deformations [249,250] of the background, and quantum deformations (in the sense of quantum groups) of the und”
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, background): “More recently, q-deformations of the psu(2|2) n R(3) algebra were considered in [57].”
An integrable deformation of the AdS5 × S5 superstring (2014, methodology): “The twobody deformed S-matrix is built out of the R-matrix of h U ( ) q written down by Beisert and Koroteev [9] in the schematic form”