A pseudo-BCS wavefunction from density matrix decomposition - application in auxilary-field quantum Monte Carlo

We present a method to construct BCS-like (pseudo-BCS) wave functions from the one-body density matrix.
The resulting many-body wave function reproduces the density matrix and has the form of a particle number-projected BCS wave function (or antisymmetrized germinal power), which can provide a better Ansatze in correlated fermion systems than a single Slater determinant or a linear combination of Slater determinants (for example from a truncated active space calculation). We apply the pseudo-BCS wave function to auxiliary-field quantum Monte Carlo (AFQMC) as a trial wave function. Using the two-dimensional Hubbard model as an example, we show that it leads to improved results as a constraint. Further, the pseudo-BCS wave function allows a fully self-consistent constraint via the density matrix.