Evaluation of the two-particle propagator for Hubbard model with the help of Hubbard-I approximation

TL;DR

This study extends the Hubbard-I approximation to evaluate the anomalous two-electron propagator in the 2D Hubbard model and compares it with quantum Monte Carlo data, finding qualitative agreement in decay behavior.

Contribution

The paper introduces a generalized Hubbard-I approximation for the two-particle propagator and assesses its accuracy against Monte Carlo results.

Findings

Hubbard-I qualitatively matches Monte Carlo decay patterns.

Decay of d-wave correlations follows a r^{-3} law beyond 2-3 lattice sites.

Hubbard-I underestimates the decay coefficient by about three times.

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 $r$.