We present the results of a self-consistent weak-coupling calculation for the renormalized single-particle properties in an itinerant antiferromagnet. Multiple spin-wave excitations accompany the carrier motion and lead to incoherent contributions to the electronic spectrum. We evaluate the quasiparticle spectral weight and energy dispersoin. In agreement with strong-coupling theories we find the minimum of the dispersion of the quasihole energy to have momentum (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) and the dispersion to be flat around the corners of the Brillouin zone. Very good agreement is achieved with available exact diagonalization data.
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\ensuremath{\gg}: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\ensuremath{\approx}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 ``string'' picture, where propagation of holes creates strings of overturned spins with which the holes interact. In the present work 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. We show that 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=(\ensuremath{\pi}/2,\ensuremath{\pi}/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, as expected when approaching the noninteracting limit. 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.
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
t2/
U2 for large U. We calculate the shape of the quasihole Fermi surface and find that it consists of four pockets around the points (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/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.
We revisit the problem of the dispersion of a single hole injected into a quantum antiferromagnet. We applied a spin-density-wave formalism extended to a large number of orbitals and obtained an integral equation for the full quasiparticle Green's function in the self-consistent ``noncrossing'' Born approximation. We found that for $t/J\ensuremath{\gg}1$, the bare fermionic dispersion is completely overshadowed by the self-energy corrections. In this case, the quasiparticle Green's function contains a broad incoherent continuum which extends over a frequency range of $\ensuremath{\sim}6t$. In addition, there exists a narrow region of width
O(JS) below the top of the valence band, where the excitations are mostly coherent, though with a small quasiparticle residue $Z\ensuremath{\sim}J/t$. The top of the valence band is located at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. We found that the form of the fermionic dispersion, and, in particular, the ratio of the effective masses near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ strongly depend on the assumptions one makes for the form of the magnon propagator. We argue in this paper that two-magnon Raman scattering as well as neutron-scattering experiments strongly suggest that the zone-boundary magnons are not free particles since a substantial portion of their spectral weight is transferred into an incoherent background. We modeled this effect by introducing a cutoff
qc in the integration over magnon momenta. We found analytically that for small
qc, the strong-coupling solution for the Green's function is universal, and both effective masses are equal to ${(4JS)}^{\ensuremath{-}1}$. We further computed the full fermionic dispersion for
J/t=0.4 relevant for
Sr2CuO2Cl2, and ${t}^{\ensuremath{'}}=\ensuremath{-}0.4J$ and found not only that the masses are both equal to ${(2J)}^{\ensuremath{-}1}$, but also that the energies at
(0,0) and $(0,\ensuremath{\pi})$ are equal, the energy at $(0,\ensuremath{\pi}/2)$ is about half of that at
(0,0), and the bandwidth for the coherent excitations is around
3J. All of these results are in full agreement with the experimental data. Finally, we found that weakly damped excitations only exist in a narrow range around $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. Away from the vicinity of $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$, the excitations are overdamped, and the spectral function possesses a broad maximum rather than a sharp quasiparticle peak. This last feature was also reported in photoemission experiments.
Results for the single-particle Green's function for the strong-coupling limit of the single-band Hubbard model ($t\ensuremath{-}J$ model) obtained by numerical and analytical methods are discussed. The numerical calculation of the spectral function is performed for small systems of up to 18 sites using the Lanczos method. A detailed analysis of the spectral functions for the $t\ensuremath{-}J$ model in one and two dimensions is given. We also investigate the effect of the next-nearest-neighbor hopping terms, which appear in order
Ut2 and are omitted in the standard $t\ensuremath{-}J$ model. The role of quantum fluctuations on the shape of the spectra and the fundamental difference between one and two dimensions is elucidated. In 2D we find evidence for a coherent quasiparticle band of width
2J with dispersion $^{\ensuremath{\omega}}\mathrm{k}\ensuremath{\sim}(\frac{J}{2}){(cos{k}_{x}+cos{k}_{y})}^{2}$ and spin
S=21, which emerges at the low-energy edge of the incoherent spectrum. This form of dispersion is due to effective next-nearest-neighbor processes related to spin flips and agrees with our extension of the approach of Brinkman and Rice to finite
J.
The temperature-dependent self-energy of the hole-doped two-dimensional Hubbard model is calculated perturbatively up to second order and used to find the spectral function for all points in the Brillouin zone. Single-particle dispersion, density of states, and Fermi surface topology are thus obtained and the appearance of the strong-coupling features studied. The renormalized quantities are temperature dependent due to an interplay between the electron correlation and topology of free-electron bands close to the Fermi energy.