Motion of a single hole in an itinerant-electron antiferromagnet

We study the propagation of a single hole in the spin-density-wave state of the half-filled two-dimensional Hubbard model. This state is insulating not because of strong electron correlations, but because of the single-particle gap caused by magnetic ordering. We calculate the self-energy of the hole in the one-loop approximation and solve the Dyson equation to extract quantities such as the quasihole spectral function, energy dispersion, and lifetime. At all values of U we find a quasiparticle peak in the hole spectral function. The strength of the peak decreases as ${\mathit{t}}^2$/${\mathit{U}}^2$ for large U. We calculate the shape of the quasihole Fermi surface and find that it consists of four pockets around the points (±π/2,±π/2). Finally, we discuss the large-U extrapolation of our theory and compare our results with those of recent mean-field theories of the strong-coupling antiferromagnet.