Interacting Electrons in a Quantum Dot: Quantum Monte Carlo Studies

摘要

An efficient optimization method for the quantum Monte Carlo many-body wave211u001efunctions, called the stochastic gradient approximation (SGA), is presented. 211u001eUsing this method, the states of interacting electrons in a semiconductor quantum 211u001edot are studied for a wide range of magnetic field values. The generally accepted 211u001emodel for the electrons in a two-dimensional semiconductor quantum dots, 211u001econsisting of a two-dimensional harmonic potential and an external magnetic 211u001efield, has been used. The variational many-body wave functions are constructed 211u001efor magentic field values starting from zero up to the limit of strong magnetic 211u001efield. The two important ingredients in the building of the wave function are 211u001efound to be the restriction of the center-of-mass motion to the lowest energy 211u001estate and the inclusion of the relative coordinates in the wave function.