Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function

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