Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant

TL;DR

This study investigates the magnetic susceptibility of the 2D Hubbard model using a power series approach, revealing incommensurate responses and ferromagnetic correlations consistent with numerical simulations and experimental observations.

Contribution

It introduces a diagram technique based on a power series in the hopping constant for analyzing strong correlations in the Hubbard model, providing new insights into magnetic properties.

Findings

Zero-frequency susceptibility matches Monte Carlo results.

No ferromagnetic correlations found in certain parameter ranges.

Incommensurate susceptibility behavior explains experimental observations.

Abstract

The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping 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. At half-filling the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately results of Monte Carlo simulations. Also in agreement with numerical simulations no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\alt\bar{n}\alt 1.2$ for the repulsion parameters $8|t|\leq U\leq 16|t|$. However, for larger $U/|t|$ and $|1-\bar{n}|\approx 0.2$ the nearest neighbor correlations become ferromagnetic. For $\bar{n}\alt 0.94$ and $\bar{n}\agt 1.06$ the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing the frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.