Fluctuating charge-density waves in the Hubbard model

Abstract

The charge susceptibility of the two-dimensional repulsive Hubbard model is investigated by using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. It is shown that once the Fermi level crosses one of the Hubbard subbands, a sharp peak appears in the momentum dependence of the static susceptibility. With further departure from half-filling, the peak transforms to a ridge around the $\ensuremath{\Gamma}$ point. Within the considered range $0\ensuremath{\le}|1\ensuremath{-}\overline{n}|\ensuremath{\lesssim}0.2$ of the electron filling $\overline{n}$, the static susceptibility is finite, which points to the absence of long-range charge ordering. However, for $|1\ensuremath{-}\overline{n}|\ensuremath{\approx}0.12$, the susceptibility maxima are located halfway between the center and the boundaries of the Brillouin zone. In this case, an interaction of the carriers with the tetragonal distortions can stabilize the charge-density wave with the wavelength of four lattice spacings, as experimentally observed in the low-temperature tetragonal phase of lanthanum cuprates. Within the range of parameters inherent in cuprate perovskites, the character of the susceptibility evolution with $\overline{n}$ depends only weakly on the ratio of the nearest-neighbor hopping constant to the Hubbard repulsion and on details of the initial band structure. The location of the susceptibility maxima in the Brillouin zone is mainly determined by the value of $\overline{n}$.