Diagonalizations on a correlated basis

Abstract

Unsymmetrical quantum-dot systems are generally difficult to study using wave-function techniques, like quantum Monte Carlo (QMC) or exact diagonalization (ED) methods. The initial trial wave function for Monte Carlo methods is difficult to find, and the exact diagonalization method can only handle very few particles. In this article a two-dimensional semiconductor quantum dot containing a non-centered impurity ion is studied, using a new exact wave-function method. Results are analyzed and compared to density-functional-theory calculations. The computational method allows one to relax the commonly used lowest-Landau level (LLL) approximation, and it's effects are studied, e.g., on the charge and current density profiles. The method, which is a combination of QMC and ED methods, is described. It combines the scalability of Monte Carlo methods with the benefits of exact diagonalization, and allows one to accurately obtain the wave function for unsymmetrical quantum dots up to more than ten electrons. Also, excited states are accessible and are analyzed in this article.