Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model

TL;DR

This study applies the coupled-cluster method to the 2D Hubbard model to evaluate its effectiveness in capturing electron correlations, showing high accuracy in weak to intermediate interaction regimes and potential for broader electronic structure calculations.

Contribution

It demonstrates the applicability of the coupled-cluster method with the ACP approximation to the 2D Hubbard model, achieving high accuracy in certain interaction regimes and suggesting its use in ab-initio band calculations.

Findings

ACP method accounts for most correlation energies at low to intermediate U/t

Error remains below 1% in these regimes

Method's accuracy is independent of system size

Abstract

We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations actually used in ab-initio band calculations. The double excitation version of the CCM, implemented using the approximate coupled pair (ACP) method, account for most of the correlation energies of the 2D Hubbard model in the weak ($U/t \simeq 1$) and the intermediate $U/t$ regions ($U/t \simeq 4$). The error is always less than 1% there. The ACP approximation gets less accurate for large $U/t$ ($U/t \simeq 8$) and/or near half-filling. Further incorporation of electron correlation effects is necessary in this region. The accuracy does not depend on the system size and the gap between the lowest unoccupied level and the highest occupied level due to the finite size effect. Hence, the CCM may be favorably applied to ab-initio band calculations on metals as well as semiconductors and insulators.