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Title: Quantum Monte Carlo Calculations Applied to Magnetic Molecules

Abstract

We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations.more » The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these ideas in hand, we then provide a detailed explanation of the current QMC method in Chapter 4. The remainder of the thesis is devoted to presenting specific results: Chapters 5 and 6 contain articles in which this method has been used to answer general questions that are relevant to broad classes of systems. Then, in Chapter 7, we provide an analysis of four different species of magnetic molecules that have recently been synthesized and studied. In all cases, comparisons between QMC calculations and experimental data allow us to distinguish a viable microscopic model and make predictions for future experiments. In Chapter 8, the infamous ''negative sign problem'' is described in detail, and we clearly indicate the limitations on QMC that are imposed by this obstacle. Finally, Chapter 9 contains a summary of the present work and the expected directions for future research.« less

Authors:
 [1]
  1. Iowa State Univ., Ames, IA (United States)
Publication Date:
Research Org.:
Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
892729
Report Number(s):
IS-T 2543
TRN: US0605860
DOE Contract Number:
W-7405-Eng-82
Resource Type:
Thesis/Dissertation
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HILBERT SPACE; MONTE CARLO METHOD; PHYSICS; SAMPLING; SIMULATION; SPIN; THERMODYNAMIC PROPERTIES

Citation Formats

Engelhardt, Larry. Quantum Monte Carlo Calculations Applied to Magnetic Molecules. United States: N. p., 2006. Web. doi:10.2172/892729.
Engelhardt, Larry. Quantum Monte Carlo Calculations Applied to Magnetic Molecules. United States. doi:10.2172/892729.
Engelhardt, Larry. Sun . "Quantum Monte Carlo Calculations Applied to Magnetic Molecules". United States. doi:10.2172/892729. https://www.osti.gov/servlets/purl/892729.
@article{osti_892729,
title = {Quantum Monte Carlo Calculations Applied to Magnetic Molecules},
author = {Engelhardt, Larry},
abstractNote = {We have calculated the equilibrium thermodynamic properties of Heisenberg spin systems using a quantum Monte Carlo (QMC) method. We have used some of these systems as models to describe recently synthesized magnetic molecules, and-upon comparing the results of these calculations with experimental data-have obtained accurate estimates for the basic parameters of these models. We have also performed calculations for other systems that are of more general interest, being relevant both for existing experimental data and for future experiments. Utilizing the concept of importance sampling, these calculations can be carried out in an arbitrarily large quantum Hilbert space, while still avoiding any approximations that would introduce systematic errors. The only errors are statistical in nature, and as such, their magnitudes are accurately estimated during the course of a simulation. Frustrated spin systems present a major challenge to the QMC method, nevertheless, in many instances progress can be made. In this chapter, the field of magnetic molecules is introduced, paying particular attention to the characteristics that distinguish magnetic molecules from other systems that are studied in condensed matter physics. We briefly outline the typical path by which we learn about magnetic molecules, which requires a close relationship between experiments and theoretical calculations. The typical experiments are introduced here, while the theoretical methods are discussed in the next chapter. Each of these theoretical methods has a considerable limitation, also described in Chapter 2, which together serve to motivate the present work. As is shown throughout the later chapters, the present QMC method is often able to provide useful information where other methods fail. In Chapter 3, the use of Monte Carlo methods in statistical physics is reviewed, building up the fundamental ideas that are necessary in order to understand the method that has been used in this work. With these ideas in hand, we then provide a detailed explanation of the current QMC method in Chapter 4. The remainder of the thesis is devoted to presenting specific results: Chapters 5 and 6 contain articles in which this method has been used to answer general questions that are relevant to broad classes of systems. Then, in Chapter 7, we provide an analysis of four different species of magnetic molecules that have recently been synthesized and studied. In all cases, comparisons between QMC calculations and experimental data allow us to distinguish a viable microscopic model and make predictions for future experiments. In Chapter 8, the infamous ''negative sign problem'' is described in detail, and we clearly indicate the limitations on QMC that are imposed by this obstacle. Finally, Chapter 9 contains a summary of the present work and the expected directions for future research.},
doi = {10.2172/892729},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}

Thesis/Dissertation:
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  • This thesis research consists of computer simulation studies of both classical and quantum many body problems. The classical problem deals with the ultrafast Kerr effect observed in molecular liquids when irradiated with high intensity picosecond laser light. A strong birefringence is induced in such a system, and this study investigates the dynamics of that response. By using the molecular dynamics simulation method to integrate Newton's equations of motion for a large ensemble of molecules, these exact simulation results to predictions from diffusion theory. The second area of investigation addresses several issues concerning the applicability of quantum simulation methods to themore » calculation of electronic ground state properties of atoms and molecules. There exists a fundamental problem in applying quantum simulation methods in fermion systems. Approximate attempts by earlier researchers have been sufficiently flawed so as to make the significance of their results ambiguous. The author reexamines the application of the Green's Function Monte Carlo method to a class of lithium-like atoms in such a way as to systematically remove the major approximations from the method. The result yields a highly accurate and reliable approach to calculation ground state properties of atoms and molecules. Specific results for three electron atoms can be compared to other theoretical calculations and experiments.« less
  • Monte Carlo methods have been widely applied to problems in nuclear physics, mathematical reliability, communication theory, and other areas. The work in this thesis is developed mainly with neutron transport applications in mind. For nuclear reactor and many other applications, random walk processes have been used to estimate multi-dimensional integrals and obtain information about the solution of integral equations. When the analysis is statistically based such calculations are often costly, and the development of efficient estimation techniques plays a critical role in these applications. All of the error reduction techniques developed in this work are applied to model problems. Itmore » is found that the nearly optimal parameters selected by the analytic method for use with GWAN estimator are nearly identical to parameters selected by the multistage method. Modified path length estimation (based on the path length importance measure) leads to excellent error reduction in all model problems examined. Finally, it should be pointed out that techniques used for neutron transport problems may be transferred easily to other application areas which are based on random walk processes. The transport problems studied in this dissertation provide exceptionally severe tests of the error reduction potential of any sampling procedure. It is therefore expected that the methods of this dissertation will prove useful in many other application areas.« less
  • A search is made for discrete subgroups of SU(2) and SU(3) for which the phase transition occurs beyond the region of physical interest. For SU(2) two subgroups are found that have a transition beyond this region. One of these, the double icosahedral group (anti I), agrees with the group SU(2) well into the asymptotic weak coupling region. No discrete subgroups suitable for approximating the group SU(3) are found to exist. A comparison is made between the group anti I and the group SU(2) to see at what order of inverse bare coupling constant squared their strong coupling expansions differ. Montemore » Carlo calculations are carried out for three discrete subgroups of SU(2). These are the double tetrahedral group (anti T), the double octahedral group (anti O), and the group anti I. Evidence for first order phase transitions is found for each of these groups and the critical value of inverse coupling squared is found. In addition anti I is seen to follow SU(2) in exhibiting asymptotic freedom behavior until its phase transition occurs. Further the results for I are numerically compared with those for SU(2) and agree very closely over a wide range of coupling. A technique is introduced by which fermion effects can be included in the calculations. The calculations are performed for anti T and anti I and the results are compared with a previously proposed method which incorporates complete fermion effects. Although the latter method is more accurate, the former uses much less computer time. The results of the two calculations are found not to differ with statistically meaningful deviations. However these two results do differ from those of pure gauge theory. Because of the particular loop that is chosen for the effective action it is concluded that these differences mainly arise from finite lattice effects.« less