A Variational Ground-State for the $\nu=2/3$ Fractional Quantum Hall Regime

TL;DR

This paper introduces a variational ground state for the $ u=2/3$ fractional quantum Hall regime, unifying different edge theories and predicting a sharp transition in the ground state observable in tunneling experiments.

Contribution

It presents a novel variational $ u=2/3$ state that combines edge theories and uses Monte Carlo methods to analyze its properties and transitions.

Findings

Identifies a sharp transition in the ground state as a function of confining potential slope.

Determines correlation functions of the $ u=2/3$ state via Monte Carlo simulations.

Predicts observable effects in tunneling experiments through quantum dots.

Abstract

A variational $\nu=2/3$ state, which unifies the sharp edge picture of MacDonald with the soft edge picture of Chang and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state and those of the Laughlin $\nu=1/3$ wavefunction, the correlation functions of the $\nu=2/3$ state are determined via a classical Monte Carlo calculation, for systems up to $50$ electrons. It is found that as a function of the slope of the confining potential there is a sharp transition of the ground state from one description to the other. This transition should be observable in tunneling experiments through quantum dots.