Quantum Monte Carlo for transition metal systems method developments and applications /

by (Lucas Kyle), 1980- Wagner

WAGNER, LUCAS K. Quantum Monte Carlo for Transition Metal Systems: Method Developments and Applications. (Under the direction of Professor Lubos Mitas). 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. Quantum Monte Carlo for Transition Metal Systems: Method Developments and Applications by Lucas K. Wagner A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Physics Raleigh 2006 Approved By: Dr. M. Buongiorno-Nardelli Dr. D. Lee Dr. L. Mitas Chair of Advisory Committee Dr. K. Ito To Marta and my parents. A Marta e ai miei genitori. ii iii Biography I was born September 21, 1980 in the city of Danville, in the southwestern part of Virginia to James and Deborah Wagner. I grew up near the town of Chatham, about 10 miles north of Danville with a population of around 1,300 people. I spent kindergarten and first grade at Chatham Elementary School, moved to Climax Elem for second through fifth, Central Middle for sixth and seventh, and finished primary schooling in Chatham High School in June of 1998. I entered North Carolina State University as a major in physics. I worked one semester for the WebAssign project, and immediately sought out a place to work in a ‘real’ lab. I approached Dr. Jacqueline Krim for a place as an undergraduate researcher and she agreed. I started in my second semester at NCSU. The first day, I leveled all the desks in her office and painted her filing cabinet. I spent some time helping her group move in and set up the lab, since she had just moved from Northeastern University. After a while, I did perform some research in her lab, none of which was probably worthy of publishing, but I very much enjoyed it. I worked on various projects, finding a quartz crystal that would still oscillate at 500 Celsius, building a ultra-high vacuum vapor deposition chamber, and ripping postdoc Brian Mason’s carefully constructed superconductivity-dependent friction experiment to pieces. In my second year of university, I started to get interested in mathematics. I ended up adding a second major of applied mathematics in that year. I was very interested in math, used with computers, to solve problems that would otherwise be intractable. This is the topic of this dissertation, so the thought has stayed with me. The thought is something like this: the computer Deep Blue was able to beat one of the best chess players in the world. Its creators are absolutely not able to beat him, and probably would not be able to come even close. I imagine that to them (and me), such a thing is just about as hard as, say, understanding the complicated motion of many many objects all interacting with each other. Nonetheless, with substantial effort, it seems to be possible to use a computer to filter a really complicated problem down to something we can handle. This dissertation is about a tiny step in that direction. In the beginning of my third year in the undergraduate curriculum, I left Dr. Krim’s lab to work with Dr. Mitas. We worked on silicon nanocrystals, which resulted in a few papers and an award from the college for the best undergraduate research. I completed my double major in physics and applied mathematics, and Dr. Mitas iv convinced me to stay on with him for my PhD work. In my second year as a doctoral candidate, I applied for and received the National Science Foundation Graduate Research Fellowship, which I have appreciated greatly. v