d-wave pairing versus stripe order in the two-dimensional Hubbard model*

We study the competition between d-wave superconducting pairing and stripe orders in the ground state of the doped two dimensional Hubbard model. Two complimentary methods, the constrained path auxiliary-field quantum Monte Carlo (CP AFQMC) and Density Matrix Renormalization Group (DMRG), are employed. Pinning fields (antiferromagnetic, pairing, or both) are applied at the edge of the lattice to induce symmetry breaking in the ground state. By detailed comparisons and cross checks, we determine the ground-state properties in large rectangular supercells. Careful extrapolations to the thermodynamic limit are then performed to quantify the long-range behavior of the pairing correlation and its relation to the spin and charge order.