Simulation of the NMR Response of Cuprates Above and Below the Superconducting Temperature

Nuclear magnetic resonance (NMR) experiments play an essential role in the study of high T_c cuprates, showing fundamentally different features in the Knight shift and the spin-lattice relaxation rate comparing to the conventional superconductors. However, to date, the theoretical and numerical analysis of the NMR response below critical temperature is limited to RPA-based calculations or phenomenological models. Here we study the temperature and doping evolution of these quantities on the two-dimensional Hubbard model using dynamical cluster approximation with Nambu formalism. We recover the suppression of the Knight shift at the pseudogap on-set temperature and its quick decrease in superconducting region. We also simulate and analysis the spin-lattice relaxation rate and the role of vertex correction in the dynamical spin susceptibility. Both the Knight shift and the spin-lattice relaxation rate are consistent with NMR experimental results of high Tc cuprates.