Particle-hole Pfaffian order in a translationally and rotationally invariant system

The PH-Pfaffian (particle-hole Pfaffian) topological order has been proposed as a candidate order for the $\ensuremath{\nu}=5/2$ quantum Hall effect. The PH-Pfaffian liquid is known to be the ground state in several coupled wire and coupled stripe constructions. No translationally and rotationally invariant models with the PH-Pfaffian ground state have been identified so far. By employing anyon condensation on top of a topological order, allowed in an isotropic system, we argue that the PH-Pfaffian order is possible in the presence of rotational and translational symmetries.