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Article Dans Une Revue Physical Review B Année : 2023

Full-counting statistics of charge fluctuations in quantum Hall states

Clément Berthiere
  • Fonction : Auteur
Benoit Estienne
William Witczak-Krempa
  • Fonction : Auteur

Résumé

We study the cumulants of the charge distribution of a subregion for two-dimensional quantum Hall states of bosons and fermions at both integer and fractional fillings, focusing on subregions with corners. Even cumulants, which include the variance, satisfy an area law with subleading corrections sensitive to finer geometric details of the subregion such as corner contributions, while at the same time probing non-trivial sum rules for general correlation functions. We perform a systematic study of such corner terms, by a combination of analytic, numerically exact, and Monte Carlo computations. We also study odd charge cumulants, for which the area-law term vanishes and distinct corner contributions appear. The observed shape dependence of the third cumulant shows nearly universal behavior for integer and fractional Laughlin Hall states in the lowest Landau level. While these states serve as our main example, many of our finding are expected to hold in considerable generality. As an illustration, we discuss properties of gapless Dirac fermions, and more general conformal field theories.

Dates et versions

hal-03871164 , version 1 (25-11-2022)

Identifiants

Citer

Clément Berthiere, Benoit Estienne, Jean-Marie Stéphan, William Witczak-Krempa. Full-counting statistics of charge fluctuations in quantum Hall states. Physical Review B, 2023, 108 (20), pp.L201109. ⟨10.1103/PhysRevB.108.L201109⟩. ⟨hal-03871164⟩
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