|Abstract:||Quantum Monte Carlo (QMC) is one of the most powerful methods for solving many body problems in Physics and Chemistry. MC sampling allows one to measure physical properties systems with very complicated wave functions that incorporate correlation between the electrons. Additionally, QMC has O(N3) scaling verses exponential scaling for methods such as Conguration Interaction and “exact diagonalization", and it’s perfect parallelism allows one to speed up computation with little effort on large parallel computers.
Our work has focused on two systems. The first is a 1D ionic Hubbard model with a complex phase diagram that we find to exhibit a ferroeletric \bond ordered" phase. A new many-body berry's phase formulation of the electronic polarization and localization is used in conjunction with QMC to analyze whether a bond order phase exists between the customary band and Mott insulating phases. The bond order and bond order correlation functions are measured to illustrate the stability of this intermediate state, and phase swapping between two degenerate states of bond order (§B) is observed. We propose that the Mott state it is unstable to bond ordering for any degree of ionicity.
The second system we have studied is a set of idealized (harmonic) and realistic quantum dots. Two idealized dots, spherical and squashed, quasi-2D structures, are analyzed. In the first QMC is contrasted with a large set of commonly used electronic structure methods including MSFT, KLI, LSDA, and CCSD, and in the second we scrutinize whether SDW states truly exist as predicted by LSDA. In conjunction with the Computational Electronics Group at the Beckman Institute, we have performed QMC calculations on realistically modeled quantum dots in the effective mass approximation. The potentials of these dots are determined using the FEM method to solve Poisson's equation and the effective mass is allowed to spatially vary in our QMC simulations. We find that in arrays of QD's, LSDA may be insufficiently accurate to determine the proper spin states of the electrons. Additionally, we illustrate that QMC has a bright future ahead of it in modeling such devices using arbitrary functions represented on grids using splines.