Application of the SD Technique for Solving a BCS-Reduced Hubbard like Hamiltonian

Abstract

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the dx2-y2 channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We present a review of the technical details of the application of the stochastic diagonalization algorithm on this problem. To verify our results obtained with the stochastic diagonalization, they are compared with the exact diagonalization results. In order to show the convergence of the stochastic diagonalization we give a detailed analysis of the behavior of physical properties with increasing number of states. Finally we study superconductivity in this BCS-reduced Hubbard model. As an indicator of superconductivity we use the occurrence of Off Diagonal Long Range Order. We study the scaling behavior of this model for various attractive interactions and in addition the dependence of the superconducting correlation functions from the filling of the system.