Analytic approach to ground state energy of charged anyon gas in strong magnetic field

Authors

Bakhodir Abdullaev, National University of UzbekistanFollow
Ulrich Rössler, Institute for Theoretical Physics, University of RegensburgFollow
Chul-Hong Park, Research Center for Dielectric and Advanced Matter Physics, Pusan National UniversityFollow
M. Musakhanov, National University of Uzbekistan

Abstract

We present analytic formulas for the ground state energy of two-dimensional (2D) anyon gas in strong magnetic field (Landau level filling factor ν_L ≤ 1). The formulas are obtained by applying harmonic potential regularization for the vanishing confinement to harmonically confined Coulomb anyon gas. In a case of absence of the Coulomb interaction our analytic result provides an exact solution. It contains a contribution of the anyon gauge field characterized by the anyon parameters ν and ν_L. In a case of presence of the Coulomb interaction we introduce a function depending on the parameters ν, ν_L and the density parameter r_s. The function is determined by fitting the Fano-Ortolani interpolation equation in the fractional quantum Hall effect regime for spin-polarized electrons and by consistence requirement with known results for the ground state energy of the 2D Coulomb Bose gas in strong magnetic field. We show that our formulas are valid not only for fermions (ν=1) but quite generally for anyons (0 ≤ ν ≤ 1).

First Page

412

Last Page

426

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Recommended Citation

Abdullaev, Bakhodir; Rössler, Ulrich; Park, Chul-Hong; and Musakhanov, M. (2020) "Analytic approach to ground state energy of charged anyon gas in strong magnetic field," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 3: Iss. 3, Article 9.
DOI: https://doi.org/10.56017/2181-1318.1121