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

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 $Δ(π,0)- Δ(π/2,π/2)$, 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 ($π/2,π/2$) 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 $U=3.1{\rm eV}$, $t=0.35{\rm eV}$.