Anomalous low-doping phase of the Hubbard model

We present results of a systematic quantum Monte Carlo study for the single -band Hubbard model. Thereby we evaluated single-particle spectra (PES and IPES), two-particle spectra (spin and density correlation functions), and t he dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow us to identify different physical regimes. Near half-filling we find an anomalous "Hubbard-I phase," where the band structure is, up to some minor modificat ions, consistent with the Hubbard-I predictions. At lower temperatures, whe re the spin response becomes sharp, additional dispersionless "bands" emerg e due to the dressing of electrons/holes with spin excitations. We present a simple phenomenological fit that reproduces the band structure of the ins ulator 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 c oncentration of approximate to 15%, i.e., the underdoped region in the phas e diagram of high-T-c superconductors. We also investigate the nature of th e magnetic ordering transition in the single-particle spectra. We show that the transition to a spin-density wave-like band structure is not accomplis hed by the formation of any resolvable "precursor bands," but rather by a ( spectroscopically invisible) band of spin-3/2 quasiparticles. We discuss im plications for the "remnant Fermi surface" in insulating cuprate compounds and the shadow bands in the doped materials.