Angular Momentum Distribution Function of the Laughlin Droplet

TL;DR

This paper investigates the angular momentum distribution in Laughlin quantum Hall states, using exact calculations for small systems and Monte Carlo methods for larger ones, revealing edge behaviors and oscillations.

Contribution

It introduces a new relationship for orbital occupation ratios in Laughlin states and compares edge predictions with numerical results.

Findings

Exact occupation numbers for small systems

Monte Carlo estimates for larger systems

Large oscillations in occupation numbers far from the edge

Abstract

We have evaluated the angular-momentum distribution functions for finite numbers of electrons in Laughlin states. For very small numbers of electrons the angular-momentum state occupation numbers have been evaluated exactly while for larger numbers of electrons they have been obtained from Monte-Carlo estimates of the one-particle density matrix. An exact relationship, valid for any number of electrons, has been derived for the ratio of the occupation numbers of the two outermost orbitals of the Laughlin droplet and is used to test the accuracy of the MC calculations. We compare the occupation numbers near the outer edges of the droplets with predictions based on the chiral Luttinger liquid picture of Laughlin state edges and discuss the surprisingly large oscillations in occupation numbers which occur for angular momenta far from the edge.