Osafile et al
Greener Journal of Science, Engineering and Technological Research Vol. 3 (4), pp. 135-143, April 2013.
ISSN: 2276-7835 © 2011 Greener Journals
Electron Interaction at Low Filling in Two Dimensions Using a Simplification of the Modified Lanczos Technique
E.O. Osafile1*, D.O. Ojuh2 and J.O.A. Idiodi3
1Department of Physics, Federal University of Petroleum Resources, Effurun, Delta State.
2Department of Basic Sciences, Benson Idahosa University, Benin city, Edo State.
3Department of Physics, University of Benin, Benin City.
*1Corresponding Author’s E-mail: eromopower @yahoo. com
In this paper, a detailed study of the dynamics of the behavior of two electrons in two dimensions is carried out. Over the years, the Hubbard model has been heavily used as one of the standard models for the study of strongly correlated electron systems. Despite this, the mechanism of interaction of these electrons in two- dimensional systems is yet to be properly understood.
Based on this clarity problem, a modification of the standard Lanczos algorithm which is slightly different, simpler and more analytical than that presented by Dagotto in his review paper is used in a concerted attempt to produce relevant results for the correlated ground state energies and wave functions and the behavior of the interacting pairs is explained with the aid of the well known single band Hubbard model. Hence this study has been able to develop, stabilize and utilize a simplified modification of the standard Lanczos technique.
From results obtained, for large and positive values of u, interaction is repulsive while it is attractive for negative values of u. The wave function can be readily obtained at the end of each step of iteration.
Keywords: Standard Lanczos technique, Hubbard model, Modified Lanczos technique, two- dimensional systems.