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An analytic approach to the ground state energy of charged anyon gases | | B. Abdullaev
; U. Roessler
; M. Musakhanov
; | | Date: |
10 Jan 2007 | | Subject: | Strongly Correlated Electrons; Mesoscopic Systems and Quantum Hall
Effect | | Abstract: | 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 (
u 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 (
u=0) our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems (
u=1) our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. | | Source: | arXiv, cond-mat/0701219 | | Services: | Forum | Review | PDF | Favorites | |
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