Quantitative investigations of the fractional quantum Hall effect ͑FQHE͒ have been limited in the past to systems containing typically fewer than 10-12 particles, except for the 1/(2pϩ1) Laughlin states. We develop a method, using the framework of the composite-fermion theory, that enables a treatment of much bigger systems and makes it possible to obtain accurate quantitative information for other incompressible states as well. After establishing the validity of this method by comparison with few-particle exact-diagonalization results, we compute the ground-state energies and transport gaps for a number of FQHE states.

A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions. The method is applied in a correlation function Monte Carlo calculation to compute ground- and excited-state energies of bosonic van der Waals clusters of up to seven particles. The calculations are performed using trial wave functions with general three-body correlations.

We find that for the pure Coulomb repulsion the composite Fermi sea at ν = 1/2 is on the verge of an instability to triplet pairing of composite fermions.It is argued that a transition into the paired state, described by a Pfaffian wave function, may be induced if the short-range part of the interaction is softened by increasing the thickness of the two-dimensional electron system.

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter λ = (e 2 /ǫl 0 )/hω c , has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions ν = 1/3 and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in n-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in p-type systems. 73.40.Hm, 73.20.Dx Typeset using REVT E X 1

A generalized diffusion Monte Carlo method for solving the many-body Schrödinger equation on curved manifolds is introduced and used to perform a 'fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the ν = 1/3 energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations. 73.20.DxTypeset using REVT E X 1

The effects of Landau-level mixing and finite thickness of the two-dimensional electron gas on the relative stability of Skyrmion and single spin-flip excitations at Landau-level filling factor ϭ1 have been investigated. Landau-level mixing is studied by fixed-phase diffusion Monte Carlo, and finite thickness is included by modifying the effective Coulomb interaction. Both Landau-level mixing and finite thickness lower Skyrmion excitation energies and favor Skyrmions with fewer spin flips. However, the two effects do not work ''coherently.'' When finite thickness is included, the effect of Landau-level mixing is strongly suppressed. ͓S0163-1829͑99͒52136-X͔ RAPID COMMUNICATIONS R8504PRB 60 V. MELIK-ALAVERDIAN, N. E. BONESTEEL, AND G. ORTIZ

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.

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