Correlations of the Current Density in Many-Body Landau Level States

TL;DR

This paper explores the correlation functions of current density in many-body Landau level states, revealing exact relationships with number density correlations and methods to extract interaction energies, applicable to both continuum and lattice systems.

Contribution

It provides an exact relationship between current density and number density correlations in Landau level states and extends the analysis to include interaction corrections and lattice systems.

Findings

Exact relationship between current and number density correlations.

Perturbative corrections for inter-particle interactions.

Method to extract interaction energy from correlation functions.

Abstract

Motivated by recent advances in quantum gas microscopy, we investigate correlation functions of the current density in many-body Landau Level states, such as the Laughlin state of the fractional quantum Hall effect. For states fully in the lowest Landau level, we present an exact relationship which shows that all correlation functions involving the current density are directly related to correlation functions of the number density. We calculate perturbative corrections to this relationship arising from inter-particle interactions, and show that this provides a method by which to extract the system's interaction energy. Finally, we demonstrate the applicability of our results also to lattice systems.