Two-particle Irreducible Effective Action Approach to Correlated Electron Systems

TL;DR

This paper applies the two-particle irreducible effective action formalism to the two-dimensional Hubbard model, incorporating quantum fluctuations up to three loops to better understand strongly correlated electron systems.

Contribution

It introduces a 2PI effective action approach to the Hubbard model, including NLO quantum fluctuations, which enhances the analysis of strongly correlated electrons.

Findings

NLO fluctuations are significant when Coulomb repulsion exceeds twice the hopping energy.

The 2PI formalism captures quantum fluctuations beyond mean-field approximations.

Numerical results highlight the importance of including higher-order fluctuations in strongly correlated regimes.

Abstract

The two-particle irreducible (2PI) effective action theories are employed to study the strongly fluctuating electron systems, under the formalism of the two-dimensional Hubbard model. We obtain the corresponding quantum 2PI effective action after the original classic action of the Hubbard model is bosonized. In our actual calculations, the 2PI effective action is expanded to three loops, in which the leading order (LO) and next-to-leading order (NLO) quantum fluctuations are included. Numerical calculations indicate that the NLO fluctuations should not be neglected when the Coulomb on-site repulsion energy is larger than two times the nearest-neighbor hopping energy.