Characterization of fractional-quantum-Hall-effect quasiparticles

Composite fermions in a partially filled quasi-Landau level may be viewed as quasielectrons of the underlying fractional quantum Hall state, suggesting that a quasielectron is simply a dressed electron, as often is true in other interacting electron systems, and as a result has the same intrinsic charge and exchange statistics as an electron. This paper discusses how this result is reconciled with the earlier picture in which quasiparticles are viewed as fractionally-charged fractional-statistics “solitons”. While the two approaches provide the same answers for the long-range interactions between the quasiparticles, the dressed-electron description is more conventional and unifies the view of quasiparticle dynamics in and beyond the fractional quantum Hall regime. [email protected] [email protected] INTRODUCTION An intriguing feature of the fractional quantum Hall effect (FQHE) [1] is the existence of two theoretical perspectives, one formulated in terms of fractionallycharged fractional-statistics quasiparticles [2, 3, 4], and the other in terms of charge −e fermions, called composite fermions [5]. Such a circumstance occurs often in physics, and experience shows that we can gain insight by exploring all consistent perspectives, since for particular purposes one or another may be advantageous. The purpose of this note is to analyze the different ways in which the two approaches mentioned above obtain the same results for a set of quantities characterizing the topological properties of a given incompressible FQHE state. The considerations below are simple and straightforward, but to the best of our knowledge have not been spelled out clearly in the literature. In both descriptions, Laughlin’s elegant and successful wave function has played a crucial role: At filling factor ν = 1/(2m+ 1), where m is an integer, the Laughlin ground state [2] is