Variational Monte Carlo Method for Coupled Quantum Dots in Magnetic Fields

The electronic properties of two-dimensional coupled quantum dots (QD) in presence of an external magnetic field are investigated using a variational Monte Carlo (VMC) method. The many-body Schr\"{o}dinger Equation with fixed model potential for coupled QDs is solved by using two-electron trial wavefunctions made of a product of two-body Jastrow term and single-particle orbitals for both singlet and triplet states. We use the steepest descent (SD) method to optimize the expectation value of energy by iteratively updating the variational parameters. In co-linear triple QDs, we show that the exchange energy between two electrons can be tuned by varying the confinement of the central dot. We also find that the electron separation in the singlet and triplet states evolve differently upon increasing the magnetic field.