Particle-hole symmetry and composite fermions in fractional quantum Hall states

TL;DR

This paper develops a composite Dirac fermion framework for fractional quantum Hall states, ensuring particle-hole symmetry and consistency with known bounds, advancing the theoretical understanding of these states.

Contribution

It introduces an effective field theory for fractional quantum Hall states that respects all symmetries, including particle-hole symmetry, and compares it with the HLR theory.

Findings

Dirac theory satisfies particle-hole symmetry in response functions.

Haldane bound is respected by Dirac theory but violated by HLR theory.

Dispersion relations from both theories are analyzed and contrasted.

Abstract

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write down an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi liquid description, we demonstrate the appearance of the Girvin--Macdonlald--Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the HLR theory is particle-hole symmetric, correlation functions obtained from HLR are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the HLR theory violate it.