Generalization of Laughlin’s Theory for the Fractional Quantum Hall Effect

Motivated by the structure of the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor ν = 1 /m (m odd), this study considers a suitable quasiparticle operator in differential form as a modified form of Laughlin’s quasiparticle operator, which reproduces the quasiparticle wave function predicted in the CF theory, without a priori assumption of the presence of CFs. A conjugate operator is also considered as a quasihole operator to derive a novel quasihole wave function for the 1 /m state. The wave functions are interpreted as an expelled electron into a different Hilbert subspace from the original Hilbert space of the Laughlin condensate, maintaining its correlation with the electrons in the condensate. The author demonstrates that ground state wavefunctions for general states at filling fractions can be constructed as coherent superpositions of coupled Laughlin condensates and their conjugates. Notably, the study shows that states previously considered as fractional quantum Hall effects of interacting CFs can be similarly treated as coupled condensates, which leads to the prediction that half filling of the lowest Landau level is a quantum critical point for phase transitions between two topologically distinct phases, each represented by different families of states.