Hole Doping Evolution of the Quasiparticle Band in Models of Strongly Correlated Electrons for the High-T$_c$ Cuprates

Quantum Monte Carlo (QMC) and Maximum Entropy (ME) techniques are used to study the spectral function $A({\bf p},\omega)$ of the one band Hubbard model in strong coupling including a next-nearest-neighbor electronic hopping with amplitude $t'/t= -0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for high-$T_c$ cuprates in the antiferromagnetic insulating regime. A quasiparticle (q.p.) band is clearly observed in the QMC analysis at the temperature of the simulation $T=t/3$, both at and away from half-filling. At a small hole density the quasiparticle dispersion resembles the result in the non-interacting limit $U/t=0$, although with reduced effective hopping amplitudes. Such narrow q.p. band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density $$ decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $ \sim 0.70$ it has crossed it entirely. The region near momentum $(0,\pi)$ and $(\pi,0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from $(0,0)$ to $(\pi,\pi)$. The evolution with hole density of the quasiparticle dispersion is in qualitative agreement with recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\pi,0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the q.p. band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the