Holomorphic quantum Hall states in higher Landau levels

TL;DR

This paper explores the mathematical relationship between quantum Hall states in higher Landau levels and the lowest Landau level, enabling easier analysis of complex many-body quantum systems.

Contribution

It establishes a unitary correspondence that maps states and operators in higher Landau levels to those in the lowest Landau level, simplifying their study.

Findings

Effective Hamiltonians in higher Landau levels can be represented using lowest Landau level quantities.

Particle densities in higher Landau levels are expressible through lowest Landau level wave functions.

The correspondence facilitates analysis of many-body quantum Hall systems.

Abstract

Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states in higher Landau levels and those in the lowest Landau level, where wave functions are holomorphic. We apply this correspondence to many-body systems, in particular we represent effective Hamiltonians and particle densities in higher Landau levels by corresponding quantities in the lowest Landau level.