Charge fluctuations in the 2D Hubbard model

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 thi s excitation is evaluated numerically; and a gap is found at k = (0, 0) whi ch 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.