Large-scale simulations of PH-Pfaffian trial wave functions

The $\nu=5/2$ fractional quantum Hall plateau is generally attributed to pairing of composite fermions. Numerics support the anti-Pfaffian topological order at this filling, but recent experiments instead indicate a PH-Pfaffian phase. A trial wave function for the latter has been proposed, but the need for projection into the lowest Landau level has severely constrained the numerically accessible system sizes. In my talk, I will first introduce a family of paired-composite-fermion trial states for \textit{any} odd Cooper-pair angular momentum, which can be efficiently projected into the lowest Landau level for large system sizes. I will then present numerical evidence that projecting the PH-Pfaffian trial state results in a gapless composite Fermi liquid.