Quantum dots, also known as "artificial atoms" are not only of
considerable technological interest but also of theoretical interest
because it is possible to go from a weak correlation to a strong
correlation regime either by increasing the relative strength of
electron-electron interaction to the external potential or by
increasing the magnetic field. We employ diffusion Monte Carlo to
study the ground and excited states of dots in various regimes and
compare the results to those from the Hartree Fock (HF) method and
from density functional theory within the local spin density
approximation (LSDA). In the absence of a magnetic field we find, in
contrast to the situation for real atoms, that the total energies and
addition energies obtained from LSDA are much more accurate than those
from HF. This is because the relative magnitude of the correlation
energy to the exchange energy is much larger in dots than in atoms and
the density is less inhomogeneous in dots. LSDA predicts reasonably
accurate excitation energies for many states, but in those cases where
the LSDA states are spin contaminated it predicts excitation energies
that are too low, whereas, in those cases where there is considerable
multideterminantal character in the excited state it predicts
excitation energies that are too high. Hund's first rule is satisfied
for all electron numbers studied, but for N=10 there is a near
degeneracy.
In the large magnetic field limit the determinants can be limited to
those arising from the lowest Landau level. For finite magnetic
fields Landau level mixing is important and can be taken into account
very effectively by multiplying the infinite-field determinants by a
Jastrow factor which is optimized by variance minimization. We apply
these wave functions to study the transition from the maximum density
droplet state (integer quantum Hall state, L=N(N-1)/2) to lower
density droplet states (L>N(N-1)/2). Composite-fermion wave
functions, projected onto the lowest Landau level and multiplied by an
optimized Jastrow factor, provide an accurate and efficient
alternative form of the wave functions.