36 research outputs found
Quantum Monte Carlo Methods in Statistical Mechanics
This paper deals with the optimization of trial states for the computation of
dominant eigenvalues of operators and very large matrices. In addition to
preliminary results for the energy spectrum of van der Waals clusters, we
review results of the application of this method to the computation of
relaxation times of independent relaxation modes at the Ising critical point in
two dimensions.Comment: 11 pages, 1 figur
Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect
The reduction of the energy gap due to Landau level mixing, characterized by
the dimensionless parameter , has
been calculated by variational Monte Carlo for the fractional quantum Hall
effect at filling fractions 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 -type GaAs, but we
conclude that Landau level mixing alone cannot account for the significantly
smaller energy gaps observed in -type systems.Comment: 11 pages, RevTex, 2 figures in compressed tar .ps forma
Skyrmion Physics Beyond the Lowest Landau Level Approximation
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 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.Comment: 4 pages, 4 figure
Masses of composite fermions carrying two and four flux quanta: Differences and similarities
This study provides a theoretical rationalization for the intriguing
experimental observation regarding the equality of the normalized masses of
composite fermions carrying two and four flux quanta, and also demonstrates
that the mass of the latter type of composite fermion has a substantial filling
factor dependence in the filling factor range , in agreement
with experiment, originating from the relatively strong inter-composite fermion
interactions here.Comment: 5 pages, 2 figure
Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
A generalized diffusion Monte Carlo method for solving the many-body
Schr\"odinger 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 energy gap and the relative stability of spin-polarized and
spin-reversed quasielectron excitations.Comment: 13 pages, Revtex + psfig, figures include
Optimization of ground and excited state wavefunctions and van der Waals clusters
A quantum Monte Carlo method is introduced to optimize excited state trial
wavefunctions. 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 upto seven particles. The calculations are performed using
trial wavefunctions with general three-body correlations
Edge reconstruction in the fractional quantum Hall regime
The interplay of electron-electron interaction and confining potential can
lead to the reconstruction of fractional quantum Hall edges. We have performed
exact diagonalization studies on microscopic models of fractional quantum Hall
liquids, in finite size systems with disk geometry, and found numerical
evidence of edge reconstruction under rather general conditions. In the present
work we have taken into account effects like layer thickness and Landau level
mixing, which are found to be of quantitative importance in edge physics. Due
to edge reconstruction, additional nonchiral edge modes arise for both
incompressible and compressible states. These additional modes couple to
electromagnetic fields and thus can be detected in microwave conductivity
measurements. They are also expected to affect the exponent of electron Green's
function, which has been measured in tunneling experiments. We have studied in
this work the electric dipole spectral function that is directly related to the
microwave conductivity measurement. Our results are consistent with the
enhanced microwave conductivity observed in experiments performed on samples
with an array of antidots at low temperatures, and its suppression at higher
temperatures. We also discuss the effects of the edge reconstruction on the
single electron spectral function at the edge.Comment: 19 pages, 12 figure