Superconducting pairing correlations in the 2D Hubbard model with next nearest hoping.

We study the superconducting pairing correlations in the ground state of the two-dimensional doped Hubbard models --- with nearest hoping t and next nearest hoping t'. Following the previous work on the pure Hubbard model, we again employ two computational methods, auxiliary field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG). These methods complement each other, and provide a powerful combination to tackle this challenging problem, where the results are sensitive to numerical details and finite size effects. We deploy our latest algorithmic advances, including a more robust procedure for self consistent constraint in AFQMC and the use of twist average boundary conditions. As a result, we achieve much higher accuracy than previously possible. We present detailed and systematic studies of the superconducting order parameter in the ground state for a number of parameter sets (t', U/t, doping), and discuss its interplay with magnetic and charge orders.