Quantum dots in high magnetic fields: Calculation of ground-state properties

Abstract

We present a variational method for calculating ground-state properties of quantum dots in high magnetic fields. Assuming a perfect spin alignment, we construct a many-body trial wave function in the form of a single Slater determinant of overlapping oscillator functions from the lowest Landau level centered around some points ${\mathbf{R}}_{i}$ inside the dot. The points ${\mathbf{R}}_{i}$ either coincide with the classical equilibrium positions or are considered as variational parameters to minimize the total energy of the system. Using these trial wave functions, we analytically calculate the ground-state properties. We present ground-state energies for up to $N=40$ electrons, compare them with available exact results for up to $N=10,$ and give a transparent interpretation of the results.