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 [1], 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', doping), and discuss its interplay with magnetic and charge orders.

[1] Mingpu Qin, Chia-Min Chung, Hao Shi, Ettore Vitali, Claudius Hubig, Ulrich Schollwöck, Steven R. White, and Shiwei Zhang, Phys. Rev. X 10, 031016 (2020)