The second-order reduced density matrix method and the two-dimensional Hubbard model

TL;DR

This paper evaluates the second-order reduced density matrix method's effectiveness in modeling the strongly correlated two-dimensional Hubbard model, demonstrating its ability to produce accurate ground state energies in intermediate correlation regimes.

Contribution

The study applies the RDM method with specific conditions to the 2D Hubbard model, showing its potential in accurately capturing strongly correlated electronic systems.

Findings

RDM method yields good ground state energies for intermediate U/t values

The method performs well with the P, Q, G, T1, and T2' conditions

Effective in the 4x4 Hubbard model case

Abstract

The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T)) accuracy without using the wave-function. One question that arises is how well does the RDM method perform with the same conditions that result in CCSD(T) accuracy in the strong correlation limit. The simplest and a theoretically important model for strongly correlated electronic systems is the Hubbard model. In this paper, we establish the utility of the RDM method when employing the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions in the two-dimension al Hubbard model case and we conduct a thorough study applying the $4\times 4$ Hubbard model employing a coefficients. Within the Hubbard Hamilt onian we found that even in the intermediate setting, where $U/t$ is between 4 and 10, the $P$, $Q$, $G$, $T1$ and $T2^\prime$ conditions re produced good ground state energies.