Advancements in the Path Integral Monte Carlo Method for Many-Body Quantum Systems at Finite Temperature
Esler, Kenneth Paul
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https://hdl.handle.net/2142/34723
Description
Title
Advancements in the Path Integral Monte Carlo Method for Many-Body Quantum Systems at Finite Temperature
Author(s)
Esler, Kenneth Paul
Issue Date
2006-10
Doctoral Committee Chair(s)
Ceperley, David M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Path integral Monte Carlo
Pseudohamiltonians
Pair Density Matrices
Language
en
Abstract
Path integral Monte Carlo (PIMC) is a quantum-level simulation method based on a stochastic sampling of the many-body thermal density matrix. Utilizing the imaginary-time formulation of Feynman's sum-over-histories, it includes thermal fluctuations and particle correlations in a natural way. Over the past two decades, PIMC has been applied to the study of the electron gas, hydrogen under extreme pressure, and supefluid helium with great success. However, the computational demand scales with a high power of the atomic number, preventing its application to systems containing heavier elements. In this dissertation, we present the methodological developments necessary to apply this powerful tool to these systems.
We begin by introducing the PIMC method. We then explain how effective potentials with position-dependent electron masses can be used to significantly reduce the computational demand of the method for heavier elements, while retaining high accuracy. We explain how these pseudohamiltonians can be integrated into the PIMC simulation by computing the density matrix for the electron-ion pair. We then address the difficulties associated with the long-range behavior of the Coulomb potential, and improve a method to optimally partition particle interactions into real-space and reciprocal-space summations.
We discuss the use of twist-averaged boundary conditions to reduce the finite-size effects in our simulations and the fixed-phase method needed to enforce the boundary conditions. Finally, we explain how a PIMC simulation of the electrons can be coupled to a classical Langevin dynamics simulation of the ions to achieve an efficient sampling of all degrees of freedom. After describing these advancements in methodology, we apply our new technology to fluid sodium near its liquid-vapor critical point. In particular, we explore the microscopic mechanisms which drive the continuous change from a dense metallic liquid to an expanded insulating vapor above the critical temperature. We show that the dynamic aggregation and dissociation of clusters of atoms play a significant role in determining the conductivity and that the formation of these clusters is highly density and temperature dependent. Finally, we suggest several avenues for research to further improve our simulations.
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