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

Two-particle Irreducible Effective Action Approach to Correlated Electron Systems