Magnetic incommensurability and fluctuating charge density waves in the repulsive Hubbard model

TL;DR

This study investigates magnetic and charge susceptibilities in the 2D repulsive Hubbard model, revealing incommensurate magnetic responses and charge maxima that resemble experimental cuprate behaviors, without long-range charge order.

Contribution

It applies a strong coupling diagram technique to analyze susceptibilities, showing incommensurability and charge maxima consistent with experiments, and clarifies that magnetic incommensurability is not due to stripes.

Findings

Incommensurate magnetic susceptibility develops with doping.

Finite charge maxima indicate absence of static charge stripes.

Magnetic incommensurability is independent of stripe formation.

Abstract

Magnetic and charge susceptibilities of the two-dimensional repulsive Hubbard model are investigated applying a strong coupling diagram technique in which the expansion in powers of the hopping constants is used. For small lattices and high temperatures results are in agreement with Monte Carlo simulations. With the departure from half-filling $x$ the low-frequency magnetic susceptibility becomes incommensurate and the incommensurability parameter grows with $x$. The incommensurability, its dependence on frequency and on $x$ resemble experimental results in lanthanum cuprates. Also for finite $x$ sharp maxima appear in the static charge susceptibility. The maxima are finite which points to the absence of the long-range charge ordering (static stripes). However, for $x\approx 0.12$ the maxima are located near the momenta $(0,\pm\pi/2)$, $(\pm\pi/2,0)$. In this case an interaction of carriers with tetragonal distortions can stabilize stripes with the wavelength of four lattice spacings, as observed in the low-temperature tetragonal phase of cuprates. As follows from the obtained results, the magnetic incommensurability is not a consequence of the stripes.