Reduced density-matrix functional theory in quantum Hall systems

TL;DR

This paper demonstrates that reduced density-matrix functional theory effectively models quantum Hall systems, accurately predicting ground states and energies, especially in strongly correlated regimes, with some limitations on detailed properties.

Contribution

It applies reduced density-matrix functional theory to quantum Hall droplets, showing its effectiveness and limitations compared to density functional theory.

Findings

One-body RDM functional method accurately predicts ground states and energies.

Results surpass density functional theory in strongly correlated regimes.

Two-body RDM method is needed for detailed properties like edge Green's function.

Abstract

We apply reduced density-matrix functional theory to the parabolically confined quantum Hall droplet in the spin-frozen strong magnetic field regime. One-body reduced density matrix functional method performs remarkably well in obtaining ground states, energies, and observables derivable from the one-body reduced density matrix for a wide range of system sizes. At the strongly correlated regime, the results go well beyond what can be obtained with the density functional theory. However, some of the detailed properties of the system, such as the edge Green's function, are not produced correctly unless we use the much heavier two-body reduced density matrix method.