Quantum Hall states in higher Landau levels

TL;DR

This paper explores the relationship between Quantum Hall states across different Landau levels, providing transformation formulas and a holomorphic function representation for states in higher levels, and discusses notable states in these levels.

Contribution

It introduces a unitary correspondence between higher and lowest Landau level states, enabling new representations and insights into Quantum Hall states in higher Landau levels.

Findings

Derived transformation formulas for densities and interactions.

Presented a holomorphic function representation for higher Landau level states.

Discussed key special Quantum Hall states in higher Landau levels.

Abstract

The unitary correspondence between Quantum Hall states in higher Landau levels and states in the lowest Landau level is discussed together with the resulting transformation formulas for particle densities and interaction potentials. This correspondence leads in particular to a representation of states in arbitrary Landau levels in terms of holomorphic functions. Some important special Quantum Hall states in higher Landau levels are also briefly discussed.