Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"

TL;DR

This paper develops a relativistic framework for the quantum Hall effect on Haldane spheres, deriving pseudopotentials and analyzing the impact of mass terms, revealing effects like the parity anomaly and state instabilities.

Contribution

It introduces a relativistic formulation of the quantum Hall effect, including explicit pseudopotential derivation and analysis of mass term effects, highlighting the parity anomaly.

Findings

Mass term interpolates between relativistic and non-relativistic regimes.

Mass term causes asymmetric effects on positive and negative Landau levels.

Laughlin state instability observed in the positive first relativistic Landau level.

Abstract

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and non-relativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly". In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.