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

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.