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We present a formulation of the Constrained Path Monte Carlo (CPMC) methodfor fermions that uses trial wave-functions that include many-body effects.This new formulation allows us to implement a whole family of generalizedmean-field states as constraints. As an example, we calculated superconductingpairing correlation functions for the two-dimensional repulsive Hubbard modelusing a BCS trial state as the constraint. We compared the results with thecase where a free-electron trial wave-function is used. We found that thecorrelation functions are independent of which state is used as the constraint,which reaffirms the results previously found by Zhang et. al regarding thesuppression of long range pairing correlations as the system size increases.Comment: 15 pages, 3 figures, submitted to Phys. Rev.

Correlated wave functions and the absence of long-range order in numerical studies of the Hubbard model