Order and fluctuations in strongly correlated quantum particle systems

Anatoli Polkovnikov

Wei‐jie Fu

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.

Nayana Shah

S K Sarker

A new functional integral mapping of a strongly correlated Fermi system to another Fermi system is presented. The strong correlations appear in the new system through momentum- and frequency-dependent coupling constants characterising correlated multi-particle motions, which can be treated perturbatively. The method is well suited to treat Hubbard and Anderson models. For the Hubbard model, the lowest-order term reproduces Hubbard's two-band Green function. Second-order processes leading to spin fluctuations are identified.

S. Hirooka, Yasuo Hamakawa

Effects of fluctuation of the superconducting order parameter in a Hubbard model are investigated in the functional-integral formalism. It is shown in the framework of the Gaussian approximation that the critical temperature is drastically reduced owing to the large fluctuations of the order parameter which originate in the strong electron correlations.

Naomichi Hatano