Single-particle excitations in a quantum antiferromagnet

Results for the single-particle Green's function for the strong-coupling limit of the single-band Hubbard model (t-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-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 t^{2}U and are omitted in the standard t-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 ^k (J2) (cos{kₗ+coskₘ) }^2 and spin S=12, 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.