Charge fluctuations in the 2D Hubbard model

Abstract

The charge susceptibility of the 2D Hubbard model is calculated by means of a Bethe-Salpeter equation within a cumulant expansion method. It is shown that in the considered approach an instability in the charge susceptibility appears and a new collective mode is generated. The energy spectrum of this excitation is evaluated numerically and a gap is found at k = (0, 0) which is a function of the Coulomb repulsion U and the doping. For any fixed U a critical value of the doping x c , at which the spectrum becomes gapless, can be determined.