Simulating Composite Fermion Excitons by Density Functional Theory and Monte Carlo on a Disk

TL;DR

This paper uses density functional theory and Monte Carlo simulations to study composite fermion excitons in fractional quantum Hall systems, revealing dispersion relations and chiral graviton excitations in disk geometry.

Contribution

It introduces a method combining DFT and Monte Carlo to analyze bulk excitations of composite fermions in FQH systems, including chiral graviton modes.

Findings

Comparison of magnetoroton dispersion with other numerical methods.

Identification of chiral graviton excitations in the spectral function.

Extension of the method to other FQH states.

Abstract

The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that experience a density-dependent effective magnetic field. This approach has been successfully applied to explore the edge rescontruction, fractional charge and fractional braiding statistics of quasiparticle excitations. In this work, we investigate composite fermion excitons in the bulk of the disk geometry. By varying the separation of the quasiparticle-quasihole pairs and calculating their energy, we compare the dispersion of the magnetoroton mode with results from other numerical methods, such as exact diagonalization (ED) and Monte Carlo (MC) simulation. Furthermore, through an evaluation of the spectral function, we identify chiral ``graviton'' excitations: a spin $-2$ mode for the particle-like Laughlin state and a spin $2$ mode for the hole-like Laughlin state. This method can be extended to construct neutral collective excitations for other fractional quantum Hall states in disk geometry.