Surprising robustness of particle-hole symmetry for composite fermion liquids

TL;DR

This study demonstrates that particle-hole symmetry in composite fermion liquids remains remarkably robust even with significant Landau level mixing, due to an effective mean-field mapping that preserves symmetry.

Contribution

The paper reveals that Landau level mixing does not significantly break particle-hole symmetry, supported by Monte Carlo calculations and a mean-field approximation that maps 3-body interactions to symmetric 2-body interactions.

Findings

Particle-hole symmetry remains nearly intact despite Landau level mixing.

A mean-field approximation captures the low-energy physics of 3-body interactions.

Constructed 2-body interactions approximate the Pfaffian wave function ground state.

Abstract

We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at $1/3$ and $2/3$. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.