Anyon with Coulomb interaction

Godfrey A. Gumbs, Danhong Huang

With the use of a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value and the Coulomb interaction is calculated in the Hartree approximation, we have calculated the coupled acoustic anyon plasmon modes for an alternating-layered interacting anyon gas structure. In a single-layer system, we obtain a phonon mode for a noninteracting anyon gas. This is different from the result given by the random- phase approximation. When the Coulomb interaction is included, this phonon mode is suppressed. In a multi-layered system, we get an acoustic anyon plasmon mode with its sound velocity renormalized by the Coulomb interaction. The uniform liquid ground state is shown to be stable against solid crystallization.

Jiannis K. Pachos

Z. F. Ezawa, Aiichi Iwazaki

In a semiclassical approximation we derive the ground-state wavefunction of the system of anyons in an external magnetic field, where anyons are interacting via the Coulomb interaction. The statistical interactions are treated in perturbation around the boson limit. The wavefunction coincides with the Laughlin wavefunction except for small corrections due to the Coulomb interaction. We also calculate the ground-state energy and the excitation spectrum.

G. Rosenberg, Babak Seradjeh, Conan Weeks +1 more

Bakhodir Abdullaev, U. Rößler, Chul‐Hong Park +1 more

We present analytic formulas for the ground state energy of two-dimensional (2D) anyon gas in strong magnetic field (Landau level filling factor νL ≤ 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 νL. In a case of presence of the Coulomb interaction we introduce a function depending on the parameters ν, νL and the density parameter rs. 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).