Ensemble Density Functional Theory for Inhomogeneous Fractional Quantum Hall Systems

TL;DR

This paper introduces an ensemble density functional approach to model large, inhomogeneous fractional quantum Hall systems, addressing the challenge of simulating finite systems with strong electron interactions.

Contribution

It presents a novel ensemble density functional method specifically designed for large, inhomogeneous FQHE systems, improving computational modeling capabilities.

Findings

Successfully models finite inhomogeneous FQHE systems with more than ten electrons.

Provides insights into the ground state properties of large, inhomogeneous fractional quantum Hall systems.

Addresses previous computational limitations in simulating complex quantum Hall phenomena.

Abstract

The fractional quantum Hall effect (FQHE) occurs at certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields strengths, the system is incompressible, i.e., there is a finite cost in energy for creating charge density fluctuations in the bulk, while the boundary of the electron gas has gapless modes of density waves. The bulk energy gap arises because of the strong electron-electron interactions. While there are very good models for infinite homogeneous systems and for the gapless excitations of the boundary of the electron gas, computational methods to accurately model finite, inhomogeneous systems with more then about ten electrons have not been available until very recently. We will here review an ensemble density functional approach to studying the ground state of large inhomogeneous spin polarized FQHE systems.