Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions

TL;DR

This paper introduces a family of parameter-free trial wave functions for particle-hole-symmetric Pfaffian states, using large-scale simulations to analyze their gapped or gapless nature in quantum Hall systems.

Contribution

The authors develop a new class of paired-composite-fermion trial wave functions applicable to various pairing symmetries, enabling efficient lowest Landau level projection and large-scale Monte Carlo analysis.

Findings

Moore-Read phase exhibits a decay length of 1.30(5) magnetic lengths.

Anti-Pfaffian phase exhibits a decay length of 1.38(14) magnetic lengths.

PH-Pfaffian shows no evidence of a finite correlation length up to 56 particles.

Abstract

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of $\xi_\text{Moore-Read}=1.30(5)$ and $\xi_\text{anti-Pfaffian}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to $56$ particles.