Finite size scaling in the tt′-Hubbard model and in BCS-reduced Hubbard models

With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses are propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz; it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with d(x)2(-y)2-wave symmetry).