Patrick Merlot, PhD student in quantum computational chemistry at UiO/CTCC

Office: UiO, Faculty of Mathematics and Natural Sciences, Department of chemistry, CTCC

Address: Universitetet i Oslo, Department of Chemistry, Postbox 1033, Blindern, 0315 Oslo, Norway

E-post: patrick.merlot (@) kjemi.uio.no

Master in Computational Physics

MANY-BODY APPROACHES TO QUANTUM DOTS

This thesis investigates numerically systems consisting of several interacting electrons in two-dimensions, confined to small regions between layers of semiconductors. These artificially fabricated electron systems are called "quantum dots" in the literature. Quantum dots provide a new challenge to theoretical calculations of their properties using many-body methods. The size of these "artificial atoms" is several orders of magnitude larger than that of atoms, leading to a much greater sensitivity to magnetic fields. The full many-body problem of quantum dots is truly complex and simulating a quantum dot constrained by a magnetic field may be even more complicated.
Of particular interest is the reliability of the Hartree-Fock (HF) method for studies of quantum dots in 2D as a function of the external magnetic field. An Hartree-Fock code for electrons trapped in a single harmonic oscillator potential in two-dimensions has been developed, as well as a code implementing many-body perturbation theory (MBPT) up to third order either directly applied to the harmonic oscillator basis or as a correction to the Hartree-Fock energy. A discussion of the results compared with large-scale diagonalisation methods indicated a quadractic error growth of HF and MBPT as the interaction strength increases. The reliability of a single Slater determinant approximation for the ground state of closed shell systems as a function of varying interaction strength has been investigated and we found that the Hartree-Fock method, compared with large-scale diagonalization methods, has a limited range of applicability as function of the interaction strength and increasing number of eletrons in the dot, indicating a break of the computational technique before entering the limit of validity of the closed-shell model.