Analytic approach to the ground-state energy of charged anyon gases

Details Analytic approach to the ground-state energy of charged anyon gases Analytic approach to the ground-state energy of charged anyon gases

2007-01-10

arxiv.org/abs/cond-mat/0701219v2

Phys. Rev. B 76, 075403 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

18 pages, 3 figures. We have added the new reference and Fig. 3 with its description in the text. The result of Fig. 3 is refl

Scientific paper

10.1103/PhysRevB.76.075403

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 leq 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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