Embedding Paired Free-Fermion Gaussian States into Gutzwiller-Projected Bardeen–Cooper–Schrieffer Wave Functions

Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) wave functions of Abrikosov fermions are widely used to describe quantum many-body states. Taking the one-dimensional transverse-field Ising model as an example, we exactly embed any even-parity spinless fermionic Gaussian state representable as a paired exponential in the chosen particle basis into a projected BCS state of spinful Abrikosov fermions. The construction provides controlled initial states for variational Monte Carlo studies of nonintegrable models.