Zusammenfassung
We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters ...
Zusammenfassung
We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters (nu and r(s), respectively). We determine this function by fitting to the ground-state energies of the classical electron crystal at very large r(s) (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small r(s). The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system (nu=0) our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems (nu=1) our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on nu, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if r(s)> 1. For r(s)<= 1 it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter nu.
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