Quantum Monte Carlo: Applications of the Twist-averaged Boundary Conditions and the Calculation of Forces
Zong, Fenghua
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https://hdl.handle.net/2142/27752
Description
Title
Quantum Monte Carlo: Applications of the Twist-averaged Boundary Conditions and the Calculation of Forces
Author(s)
Zong, Fenghua
Issue Date
2002-01
Director of Research (if dissertation) or Advisor (if thesis)
Ceperley, David M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Quantum Monte Carlo (QMC)
Twist-averaged boundary condition (TABC)
Language
en
Abstract
Quantum Monte Carlo(QMC) method is a powerful simulation tool for studying the properties of physical and chemical systems. The application of QMC to extended systems subjects to finite size effects because the simulation is often done with a small system in a super cell geometry. Periodic boundary condition is commonly used in such a setup which leads to large and fluctuating finite size error. Twist-averaged boundary condition(TABC) averages over all the possible twist angles in the boundary condition and could significantly reduce the finite size effects. In this thesis, we apply TABC to four different physical systems: the three dimensional electron gas(3DEG), the two dimensional electron gas(2DEG), the liquid 3He and the electronic surface. We studied the spin polarization transition of 3DEG with optimized wavefunctions including backfiow and three-body correlations. We found electrons spontaneously polarize at low densities. The transition starts at r 8 = 55±5. For 2DEG, we calculated the critical magnetic field that polarize the system at higher densities and determined the effective Lande g factor. At the experimental equilibrium density of liquid 3He, we computed the spin polarization energy and found the unpolarized state is stable, in agreement with experiments. We also studied the electronic energy in a slab geometry using both density functional theory within the local density approximation
and variational Monte Carlo. In all these systems, we found the finite size effects are much smaller when TABC is used. The extrapolation to the thermodynamic limit also becomes a smooth function. On another topic, we propose a method to calculate electronic forces using path integral Monte Carlo and applied it to study the hydrogen-hydrogen interaction in an electron gas.
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