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

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). 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 and real materials as examples.