Ground state energy and quasiparticle gaps in $\nu={N\over{2N\pm 1}}$ FQHE states

TL;DR

This paper investigates the scaling behavior of ground state energy and quasiparticle gaps in certain fractional quantum Hall states, revealing a nontrivial dependence on interaction potential and aligning with recent experimental results.

Contribution

It introduces a new analysis of quasiparticle energies in FQHE states using fermion operator transformations, highlighting a nontrivial potential dependence.

Findings

Exponent η > 1 for cusp shape depends on interaction potential

Quasiparticle gaps match recent experimental measurements

Scaling behavior converges towards half filling state

Abstract

Applying the transformation of fermion operators to new fermion quasiparticles introduced by Halperin, Lee, and Read we estimate a scaling behavior of the ground state energy and quasiparticle gaps as a function of filling fraction for a "principal sequence" of FQHE $\nu={N\over{2N\pm 1}}$ states converging towards the gapless state at half filling. The exponent describing the shape of the cusp $\delta E(\nu)\sim |\delta\nu|^{\eta}$ is found to be greater than one and to depend nontrivially on the interaction potential. The dependence of quasiparticle gaps agrees with the results of recent measurements by R.R.Du et al.