Evaluation of the two-particle propagator for Hubbard model with the help of Hubbard-I approximation
arXiv:0911.1631 · doi:10.1016/j.physc.2009.11.144
Abstract
The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for Hubbard model on two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada [J. Phys. Soc. Jpn. {\bf 76}, 113708 (2007)] in the limit of strong electron-electron interaction. The Hubbard-I predictions are in a good qualitative agreement with the Monte Carlo results. In particular, $d$-wave correlations decay as $c r^{-3}$ ("free electron" behaviour), if separation $r$ exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates coefficient $c$ by a factor of about three. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of $r$.
17 pages, 5 figures; the text is reorganized somewhat as compared to the preprint's previous version; an extra figure is added; some figures are re-drawn for different parameter values; typeset with IOP style