  We present a method to construct pseudo-BCS wave functions from the one-body
density matrix. The resulting many-body wave function, which can be produced
for 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 fermion
systems than a single Slater determinant, and often better than a linear
combination of Slater determinants (for example from a truncated active space
calculation). We describe a procedure to build such a wave function
conveniently from a given reduced density matrix of the system, rather than
from a mean-field solution (which gives a Slater determinant for repulsive
interactions). The pseudo-BCS wave function thus obtained reproduces the
density matrix or minimizes the difference between the input and resulting
density matrices. One application of the pseudo-BCS wave function is in
auxiliary-field quantum Monte Carlo (AFQMC) calculations as the trial wave
function to control the sign/phase problem. AFQMC is often among the most
accurate general methods for correlated fermion systems. We show that the
pseudo-BCS form further reduces the constraint bias and leads to improved
accuracy compared to the usual Slater determinant trial wave functions, using
the two-dimensional Hubbard model as an example. Furthermore, the pseudo-BCS
trial wave function allows a new systematically improvable self-consistent
approach, with pseudo-BCS trial wave function iteratively generated by AFQMC
via the one-body density matrix.
