Scaling Relations for Gaps in Fractional Quantum Hall States

TL;DR

This paper tests scaling relations for energy gaps in fractional quantum Hall states using a microscopic model, providing insights into how these gaps relate within and across different fractional sequences.

Contribution

It verifies the predicted scaling relations for quantum Hall gaps in a realistic electron system with a model potential cutoff.

Findings

Confirmed scaling relations within the same sequence.

Validated cross-sequence gap relations.

Enhanced understanding of fractional quantum Hall gap behavior.

Abstract

The microscopic approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.