Correlations in planar quantum dots: a quantum Monte Carlo study

Cyrus Umrigar, Cornell University, Ithaca, U.S.A.

Mardi 27 septembre 2005, 11^h00

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. For strongly correlated dots, highly spin-polarized states, that require promoting electrons between non-interacting shells, become nearly degenerate with the Hund's rule state.
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.