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
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