| Many properties of the two-dimensional Hubbard model have been explored for the model parameters appropriate for strongly correlated electronic systems, especially cuprate superconductors. Most of the calculations are done using a well-established dynamical cluster quantum Monte Carlo method. Using this method, we investigate the effect of long-range hoppings on superconductivity with and without the presence of phonons on small clusters. The superconducting transition temperature, Tc, is found to generally decrease with a negative next nearest neighbor hopping, t'. In the presence of the Holstein phonons, a finite t' enhances Tc in the under-doped region for the hole-doped system, consistent with band structure calculations and experiment. The validity of the spin-susceptibility-mediated pairing in this model is studied and found to yield symmetries other than d-wave when a finite t' is considered. A new numerical algorithm for solving the embedded cluster problems is introduced, and used to calculate the thermodynamic properties of the model on larger clusters, especially those associated with the quantum critical behavior at finite doping. Our results suggest that the quantum critical point (QCP) which separates the Fermi liquid and pseudogap regions, is the second order terminus of the line of first order phase separation transition in the limit when a positive t' goes to zero. For small t', the superconducting dome is centered at the QCP, suggesting that charge fluctuations might have a role in the pairing mechanism in this model. |
