Partition noise and statistics in the fractional quantum Hall effect

This paper develops a microscopic theory of current partition in fractional quantum Hall liquids, characterized by chiral Luttinger liquids, to compute the noise correlations utilizing the Keldysh technique. The investigation is conducted in a Hanbury-Brown and Twiss geometry, specifically at Laughlin filling factors ν = 1/m. The results reveal that the real-time noise correlator manifests oscillations that persist over significantly longer time scales than those observed in an uncorrelated Hall fluid. At the filling factor 1/3, the zero-frequency noise correlations exhibit negative values, indicative of anti-bunching similar to bare electrons, albeit with a markedly reduced amplitude. Moreover, these correlations transition to positive (bunching) for filling factors ν ≤ 1/5, suggesting a tendency towards bosonic behavior. The findings provide critical insights into the underlying statistics of the fractional quantum Hall effect, enhancing the understanding of the quasiparticles' nature and contributing valuable knowledge to the field of condensed matter physics.