The Nonperiodic Anyon Model and the Fractional Quantum Hall Effect

TL;DR

This paper explores a nonperiodic anyon model considering finite-size flux tubes, leading to new insights into the fractional quantum Hall effect and reproducing known series without higher Landau levels.

Contribution

It introduces a nonperiodic anyon model with finite-size effects, deriving FQHE series and reproducing Jain's series without higher Landau levels.

Findings

Reproduces Jain's series without higher Landau levels

Proposes new FQHE series, including particle-hole complementary series

Shows finite-size effects cause nonperiodic continuation of the inverse relation

Abstract

The lowest-Landau-level anyon model becomes nonperiodic in the statistics parameter when the finite size of the attached flux tubes is taken into account. The finite-size effects cause the inverse proportional relation between the critical filling factor and the statistics parameter to be nonperiodically continued in the screening regime, where the fluxes are anti-parallel to the external magnetic field -- at critical filling, the external magnetic field is entirely screened by the mean magnetic field associated with the flux tubes. A clustering argument is proposed to select particular values of the statistics parameter. In this way, IQHE and FQHE fillings are obtained in terms of gapped nondegenerate LLL-anyonic wave functions. Jain's series are reproduced without the need to populate higher Landau levels. New FQHE series are proposed, like, in particular, the particle-hole complementary series of the Laughlin one. For fast-rotating Bose-Einstein condensates, a corresponding clustering argument yields particular fractional filling series.