Electron correlation effects on Lehmann spectra of one-body Green functions for insulating states caused by the Coulomb repulsion

Abstract

Electron correlation effects on the Lehmann spectra of the one-body Green functions are clarified by using the quantum Monte Carlo simulation of path-integral form. Through the analysis of the Lehmann spectrum, we also show that the electron states of the insulating systems caused by the Coulomb repulsion (Mott-type insulators) significantly depend on the strength of the Coulomb interaction. Specifically, it is shown that in the weak interaction regime, the momentum-specified Lehmann spectrum is qualitatively explained by the second order perturbation theory from the unrestricted Hartree-Fock state, especially near the Fermi energy. This means that the Lehmann spectrum still has a dominant one-body component. On the other hand, in the strong interaction regime, the Lehmann spectrum loses such a one-body component almost completely even near the Fermi energy, and is constituted of the many-body component caused by the coupling between the charge and magnetic excitations. These results indicate that in the weak interaction regime, the electron state of the Mott-type insulator can be described by the one-body picture near the Fermi energy, while in the strong interaction regime, such a one-body picture no longer works even near the Fermi energy. For these two cases, the Lehmann spectra have clearly different peak structures. Since the Lehmann spectrum corresponds to the photoemission spectrum in experiment, we conclude that photoemission spectroscopy can be a valuable tool to obtain direct information on the strength of the Coulomb interaction.