Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2-d, a highly unconventional quadruple-fermion non-Cooper-pair order parameter is discovered.
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