  We present two 2-body Hamiltonians that approximate the exact PH-Pfaffian
wavefunction with their ground states for all the system sizes where this
wavefunction has been numerically constructed to date. The approximate
wavefunctions have high overlap with the original and reproduce well the
low-lying entanglement spectrum and structure factor. The approximate
generating Hamiltonians are obtained by an optimisation procedure where three
to four pseudopotentials are varied in the neighbourhood of second Landau level
Coulomb interaction or of a non-interacting model. They belong to a finite
region in the variational space of Hamiltonians where each point approximately
generates the PH-Pfaffian. We diagonalize the identified Hamiltonians for up to
20 electrons and find that for them the PH-Pfaffian shift appears energetically
more favorable. Possibility to interpret the data in terms of composite
fermions is discussed.
