Quantum Monte Carlo for Transition Metal Systems: Method Developments and Applications

Abstract

Quantum Monte Carlo (QMC) is a powerful computational tool to study correlated systems of electrons, allowing us to explicitly treat many-body interactions with favorable scaling in the number of particles. It has been regarded as a benchmark tool for condensed matter systems containing elements from the first and second row of the periodic table. It holds particular promise for the more complicated transition metals, because QMC treats the correlations between electrons explicitly, and has a computational cost that scales well with the system size.

We have developed a QMC framework that is capable of simulating systems containing many electrons efficiently, through advanced algorithms and parallel operation. This framework includes a QMC program using state of the art methods that make many interesting quantities available.

We apply a method of finding the minimum and other properties of the potential energy surface in the face of stochastic noise using Bayesian inference and the total energy. We apply these developments to several transition metal systems, including the first five transition metal monoxide molecules and two interesting ABO3 perovskite solids: BaTiO3 and BiFeO3.

Where experiment is available, QMC is generally in agreement with a few exceptions that are discussed. In the case where experiment is unavailable, it makes predictions that can help us understand somewhat ambiguous experimental results.