  We present results of a systematic Quantum-Monte-Carlo study for the
single-band Hubbard model. Thereby we evaluated single-particle spectra (PES &
IPES), two-particle spectra (spin & density correlation functions), and the
dynamical correlation function of suitably defined diagnostic operators, all as
a function of temperature and hole doping. The results allow to identify
different physical regimes. Near half-filling we find an anomalous `Hubbard-I
phase', where the band structure is, up to some minor modifications, consistent
with the Hubbard-I predictions. At lower temperatures, where the spin response
becomes sharp, additional dispersionless `bands' emerge due to the dressing of
electrons/holes with spin excitatons. We present a simple phenomenological fit
which reproduces the band structure of the insulator quantitatively. The Fermi
surface volume in the low doping phase, as derived from the single-particle
spectral function, is not consistent with the Luttinger theorem, but
qualitatively in agreement with the predictions of the Hubbard-I approximation.
The anomalous phase extends up to a hole concentration of 15%, i.e. the
underdoped region in the phase diagram of high-T_c superconductors. We also
investigate the nature of the magnetic ordering transition in the single
particle spectra. We show that the transition to an SDW-like band structure is
not accomplished by the formation of any resolvable `precursor bands', but
rather by a (spectroscopically invisible) band of spin 3/2 quasiparticles. We
discuss implications for the `remnant Fermi surface' in insulating cuprate
compounds and the shadow bands in the doped materials.
