Hubbard one-particle Green function in the antiferromagnetic phase

An analytic approach is presented of electronic one-particle spectra of the one-band Hubbard model at half filling in the antiferromagnetic phase. Starting from the strong-coupling regime U>t, a projection technique is used to set up self-consistent coupled equations for the electron Green function, which are valid down to values U∼t. The self-consistent equation for the hole propagator is a direct generalization of the one found from the t-J model. This gives further support to the open-quotes stringclose quotes picture, where propagation of holes creates strings of overturned spins with which the holes interact. Hopping of holes (or electrons) with up spin on the down sublattice is also taken into acount, as well as transitions between the lower and upper Hubbard bands. These are shown to change significantly the incoherent part of the t-J model spectra, by smearing out the shake-off peaks, reminiscent of higher bound string states due to multispin scattering. Coherent (quasiparticle) peaks exist at the band edges, on both sides of the insulating gap. With decreasing U the quasiparticle concept loses its meaning for wave vectors at the center of the magnetic Brillouin zone (MBZ). For large values of U the dispersion of the quasiparticle is found to scale with its band width, which is of order J. Extrema are always found at k=(π/2,π/2). The weight of the quasiparticle at this k value decreases logarithmically with increasing U. In the strong-coupling limit the spectrum tends to be symmetric, i.e., to become an even function of the frequency around the chemical potential, for any wave vector. For small values of U the dispersion at the edge of the MBZ flattens away. The spectral function in this regime, for wave vectors away from the edge of the MBZ, is concentrated mainly on one side of the chemical potential. copyright 1996 The American Physical Society