Particle-Hole Symmetric Pfaffian*

A recent experiment of Banerjee et al. [Nature 559, 205 (2018)] measured the thermal Hall conductance to be 5/2 for the ν=5/2 fractional quantum Hall effect. This observation is compatible with the particle-hole symmetric Pfaffian topological order where the chirality of the Majorana edge mode is reversed with respect to that of the Pfaffian. The particle-hole symmetric Pfaffian has not appeared as a viable candidate for the stable gapped phase at ν=5/2 in any numerical calculations for a disorder free system. We construct the particle-hole symmetric Pfaffian wavefunction in sphere and torus geometries for a number of system sizes and study its properties and further investigate the prospect of a particle-hole symmetric Pfaffian topological phase in clean systems.