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We report on fixed phase diffusion Monte Carlo calculations that show that,even for a large amount of Landau level mixing, the energies of the Pfaffianand anti-Pfaffian phases remain very nearly the same, as also do the excitationgaps at $1/3$ and $2/3$. These results, combined with previous theoretical andexperimental investigations, indicate that particle hole (PH) symmetry forcomposite fermion states is much more robust than a priori expected, emergingeven in models that explicitly break PH symmetry. We provide insight into thisfact by showing that the low energy physics of a generic repulsive 3-bodyinteraction is captured, to a large extent and over a range of filling factors,by a mean field approximation that maps it into a PH symmetric 2-bodyinteraction. This explains why Landau level mixing, which effectively generatessuch a generic 3-body interaction, is inefficient in breaking PH symmetry. As abyproduct, our results provide a systematic construction of a 2-bodyinteraction which produces, to a good approximation, the Pfaffian wave functionas its ground state.

Surprising robustness of particle-hole symmetry for composite fermion liquids