Monte Carlo comparison of quasielectron wave functions

Abstract

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions ν = 1/3, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interactions the results obtained using these two wave functions are essentially the same, though the energy gap obtained using the composite fermion quasielectron is slightly smaller, and closer to extrapolated exactdiagonalization results.

Nature of quasiparticle excitations in the fractional quantum Hall effect

“…This result is consistent with previous studies, which also reached the conclusion that the CF wave function has lower energy. [6][7][8] It is of interest to note that the energy of ⌿ L 1qp is higher than that of ⌿ CF 1qp by approximately 15% of the quasiparticle energy (ϳ0.07). ͑We note that an earlier calculation 8 on the sphere obtained a difference of Ϸ0.005 between the two quasiparticle wave functions; the reason for the discrepancy is unclear.…”

“…Different candidate theories for the charged quasiparticle excitations of the incompressible quantum Hall states have been studied in the past. [3][4][5][6][7][8] Two competing views are as follows. In Ref.…”

Berry phases for composite fermions: Effective magnetic field and fractional statistics

“…The wave function for the CF quasiparticle at =1/m written by Jain 8 is known to be more accurate than the one suggested by Laughlin. [15][16][17][18] An important step in the clarification of the issue of fractional statistics was taken by Kjønsberg and Leinaas, who showed that when the former wave function is used for a calculation of the statistics, a definite value is obtained. 19 The present study confirms that the result is robust to projection into the lowest Landau level, sorts out certain subtle corrections left out in the earlier study, and extends the calculation to more complex excitations of other incompressible states.…”

Method of computation of energies in the fractional quantum Hall effect regime

“…The aim of determining ground state energies for FQHE electron systems has been the object of many investigations with various computational methods such as exact diagonalization [10][11][12][13][14], density matrix renormalization group [15] or Monte Carlo simulations [16][17][18]. However, it is worth notifying that at the level of quasiparticle state, certain discrepancy is observed between the results of [19] using spherical geometry and the results of [20] using disk geometry, while the authors of [20] have found the reason of the discrepancy to be unclear. Also, all these methods are numerical and one may wonder whether it is possible to perform analytical methods that would serve as reliable comparison instruments even for small systems of electrons.…”