Fluctuating charge density waves in the Hubbard model

TL;DR

This paper investigates charge susceptibility in the 2D Hubbard model, revealing how peaks in susceptibility relate to charge density wave formation and their dependence on electron filling and interactions.

Contribution

It introduces a diagram technique for strong correlations to analyze charge susceptibility and links susceptibility peaks to charge density wave stabilization in cuprates.

Findings

Sharp susceptibility peaks occur when the Fermi level crosses Hubbard subbands.

Susceptibility maxima shift with electron filling, indicating potential charge density wave formation.

Charge susceptibility behavior is weakly dependent on hopping-to-interaction ratio and band structure details.

Abstract

The charge susceptibility of the two-dimensional repulsive Hubbard model is investigated 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 $\Gamma$ point. In the considered range $0\leq|1-\bar{n}|\alt 0.2$ of the electron filling $\bar{n}$ the static susceptibility is finite which points to the absence of the long-range charge ordering. However, for $|1-\bar{n}|\approx 0.12$ the susceptibility maxima are located halfway between the center and the boundaries of the Brillouin zone. In this case an interaction of carriers with tetragonal distortions can stabilize the charge density wave with the wavelength of four lattice spacings, as observed experimentally in the low-temperature tetragonal phase of lanthanum cuprates. In the range of parameters inherent in cuprate perovskites the character of the susceptibility evolution with $\bar{n}$ 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 $\bar{n}$.