Importance of local correlations for the order parameter of high-Tc superconductors

It is shown that local temporal correlations in addition to non-local spatial correlations are important to understand the size and the doping dependence of the d-wave superconducting order parameter of high-temperature superconductors. To this end, the hole- and electron-doped two-dimensional Hubbard model at zero temperature is considered and treated by an extension of the variational cluster approximation. Within this approach, the effects of temporal correlations can be studied systematically and in a thermodynamically consistent way by comparing results obtained from different reference clusters. Contact can be made with previous cellular (plaquette) dynamical mean-field calculations. This shows that temporal correlations considerably decrease the order parameter and provide a substantial gain of binding energy. Besides, a few methodical insights regarding real-space quantum-cluster approaches are obtained in addition.