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 $\nu =5/2$ 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.

Figure 1

Emergence of the PH-Pfaffian edge structure. Left panel: edge modes of two noninteracting layers with the anti-Pfaffian and Laughlin orders. Right panel: the counterpropagating modes ${\varphi }_n$ and $b$ are gapped out, and the remaining two modes exhibit the edge structure of a PH-Pfaffian liquid.

Figure 2

A coupled-stripe construction of the PH-Pfaffian order. The red lines with arrows represent interactions which gap out the connected modes.