Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach

We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit algorithm. The first determinant state is identical to that of the Hartree-Fock theory. Calculations for two-dimensional Hubbard model serve as a demonstration.