Interacting electrons in a quantum dot : quantum Monte Carlo studies

Ari Harju

P. A. Maksym

Alev Devrim Güçlü, Gun Sang Jeon, Cyrus J. Umrigar +1 more

Alev Devrim Güçlü, Jian‐Sheng Wang, Hong Min Guo

We report diffusion quantum Monte Carlo (DQMC) calculations of disordered quantum dots in the presence of an external magnetic field. The addition spectra, spin configuration, Hund's rule, and many-body densities are investigated up to 13 electrons. The data from DQMC is in excellent agreement with exact diagonalization for disorder-free quantum dots, and in marked difference with those obtained from unrestricted Hartree-Fock method. The energetic competition to electron-electron interaction due to disorder is found to change the transition energy between spin states, but the closed shell Hund's rule is maintained for the disorder strength considered here. The DQMC many-body density is found to be rather smooth.

F. Bolton

A system of N=2--4 interacting electrons in a quantum dot, with applied magnetic field, is treated using a quantum Monte Carlo method. The standard fixed-node Monte Carlo approach is modified to facilitate the inclusion of a magnetic field giving rise to a fixed-phase approximation which is introduced here. By making use of this approximation, results whose accuracy is comparable to that of exact diagonalization can be obtained. A simple set of coordinates for the four-particle problem is also used which facilitates finding a symmetrized basis. \textcopyright{} 1996 The American Physical Society.

John B. Shumway

We present a many-body computational technique for simulating interacting electrons in non-parabolic semiconductor bands. The technique uses an imaginary time propagator for a non-parabolic electron band that is described by an energy dependent effective mass. This derivation exploits a mathematical analogy between the kinetic energy with effective mass corrected to first order in energy and the relativistic kinetic energy. The propagator can be used in ground state and finite temperature quantum Monte Carlo (QMC) algorithms. We give a demonstration of this path integral QMC technique applied to interacting electrons in a self-assembled InGaAs quantum dot.