Mapping interacting onto non-interacting quantum Hall systems

TL;DR

This paper establishes a duality between interacting and non-interacting quantum Hall systems, providing analytical expressions for ground state energy and excitation gap, enhancing understanding of the composite fermion model.

Contribution

It introduces an explicit duality transforming interacting quantum Hall systems into non-interacting ones by incorporating interactions into an effective gauge field.

Findings

Derived analytic expressions for ground state energy and excitation gap.

Found good agreement with existing results across various interactions.

Provided a microscopic basis for the composite fermion model.

Abstract

We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective magnetic vector potential. The result is analogous to, and illuminates the microscopic origin of, the well-known composite fermion model, but has several advantageous properties. Using this duality we derive, for an arbitrary short-range interaction, analytic expressions for the ground state energy and the excitation gap as functions of the filling fraction. We find good agreement with existing results.