Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Matrix product states (MPS) and `dressed' ground of quadratic mean fields (e.g. Gutzwiller projected Slater Determinants) are both important classes variational wave-functions. This latter class has played roles in understanding superconductivity quantum spin-liquids. We present a novel method to obtain the finite infinite MPS (iMPS) representation state an arbitrary fermionic mean-field Hamiltonian, (which simplest case is determinant most general Pfaffian). also show how represent products such determinants times Pfaffians). From this one can project single occupancy evaluate entanglement spectra after projection. then iMPS that arise from slave-fermion approach $S=1$ Bilinear-Biquadratic (BLBQ) spin chain. To accomplish this, we develop orthogonalize degenerate find all ground-state manifold. energies match closely indicating accurate there minimal loss due truncation error. first exploration exploring their qualitative features finding good agreement with respective exact found DMRG.