Magnon and Hole Excitations in the Two-Dimensional Half-filled Hubbard Model

TL;DR

This paper investigates the excitation spectra of the half-filled Hubbard model, revealing how charge fluctuations influence spin spectra, and provides parameters fitting experimental data for La$_2$CuO$_4$.

Contribution

It offers new insights into the spin and hole excitations in the Hubbard model, especially regarding the sensitivity of high energy spin spectra to charge fluctuations and parameter fitting to experimental data.

Findings

High energy spin spectra are sensitive to charge fluctuations.

The energy difference $ ext{Δ}( ext{π},0)- ext{Δ}( ext{π/2}, ext{π/2})$ changes sign at $t/U oughly 0.053$.

The hole bandwidth is proportional to $J$ and larger than in t-J models.

Abstract

Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as a function of $t/U$. We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference $\Delta(\pi,0)- \Delta(\pi/2,\pi/2)$, which is negative for the Heisenberg model, changes sign at a fairly small $t/U\approx 0.053(5)$. The hole bandwidth is proportional to $J$, and considerably larger than in the t-J models. It has a minimum at ($\pi/2,\pi/2$) and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in La$_2$CuO$_4$ at $T=10K$ is obtained with the parameter values $U=3.1{\rm eV}$, $t=0.35{\rm eV}$.