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We present a method to construct pseudo-BCS wave functions from the one-bodydensity matrix. The resulting many-body wave function, which can be producedfor any fermion systems, including those with purely repulsive interactions,has the form of a number-projected BCS form, or antisymmetrized germinal power(AGP). Such wave functions provide a better ansatz for correlated fermionsystems than a single Slater determinant, and often better than a linearcombination of Slater determinants (for example from a truncated active spacecalculation). We describe a procedure to build such a wave functionconveniently from a given reduced density matrix of the system, rather thanfrom a mean-field solution (which gives a Slater determinant for repulsiveinteractions). The pseudo-BCS wave function thus obtained reproduces thedensity matrix or minimizes the difference between the input and resultingdensity matrices. One application of the pseudo-BCS wave function is inauxiliary-field quantum Monte Carlo (AFQMC) calculations as the trial wavefunction to control the sign/phase problem. AFQMC is often among the mostaccurate general methods for correlated fermion systems. We show that thepseudo-BCS form further reduces the constraint bias and leads to improvedaccuracy compared to the usual Slater determinant trial wave functions, usingthe two-dimensional Hubbard model as an example. Furthermore, the pseudo-BCStrial wave function allows a new systematically improvable self-consistentapproach, with pseudo-BCS trial wave function iteratively generated by AFQMCvia the one-body density matrix.

A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo