Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems

TL;DR

This paper numerically investigates charge neutral excitations in fractional quantum Hall systems, revealing multiple magnetoroton peaks in certain Jain states and verifying a sum rule linking guiding center spin to spectral densities.

Contribution

It uncovers multiple magnetoroton peaks in the spectra of specific Jain states and confirms a sum rule connecting guiding center spin with spectral densities.

Findings

Two magnetoroton peaks in $ u=2/7$ and $ u=2/9$ states

Opposite chiralities of magnetorotons in $ u=2/7$

Verification of a sum rule relating guiding center spin and spectral densities

Abstract

We study numerically the the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, $\nu=2/7$ and $\nu=2/9$, and the $\nu=1/4$ Fermi-liquid state itself. In contrast to the $\nu=1/3$ states and the Jain states near half filling, on each of the two Jain states $\nu=2/7$ and $\nu=2/9$ the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the $\nu=2/7$ state and the same chirality in the $\nu=2/9$ state. We also provide a numerical verification of a sum rule relating the guiding center spin $\bar s$ with the spectral densities of the stress tensor