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We present a simple and stable numerical method to approximate the groundstate of a quantum many-body system by multiple determinant states. This methodsearches these determinant states one by one according to the matching pursuitalgorithm. The first determinant state is identical to that of the Hartree-Focktheory. Calculations for two-dimensional Hubbard model serve as ademonstration.

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