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Title:  Path integral Monte Carlo and the electron gas 
Author(s):  Brown, Ethan 
Director of Research:  Ceperley, David M. 
Doctoral Committee Chair(s):  Hughes, Taylor L. 
Doctoral Committee Member(s):  Ceperley, David M.; Cooper, S. Lance; DuBois, Jonathan; Schleife, Andre 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Path integral Monte Carlo
electron gas quantum Monte Carlo electronic structure 
Abstract:  Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finitetemperature. By stochastically sampling Feynman's path integral representation of the quantum manybody density matrix, path integral Monte Carlo includes nonperturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, highpressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finitetemperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixednode constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warmdense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finitetemperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixednode approximation. As a first step, we utilize the variational principle inherent in the path integral Monte Carlo method to optimize the nodal surface. By using a ansatz resembling a free particle density matrix, we make a unique connection between a nodal effective mass and the traditional effective mass of manybody quantum theory. We then propose and test several alternate nodal ansatzes and apply them to single atomic systems. Finally, we propose a method to tackle the sign problem head on, by leveraging the relatively simple structure of permutation space. Using this method, we find we can perform exact simulations this of the electron gas and $^3$He that were previously impossible. 
Issue Date:  20140916 
URI:  http://hdl.handle.net/2142/50560 
Rights Information:  Copyright 2014 Ethan Brown 
Date Available in IDEALS:  20140916 
Date Deposited:  201408 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois