My PhD thesis - Condensed Matter Theory - Imperial College London

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CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS 0.06 LDA VMC n(z) 0.04 0.02 0 0 s z Figure 8.14: The electron density profile, from LDA and VMC. The wave function used in VMC was a product of determinants made up of LDA orbitals, with no Jastrow factor; the densities are the same, to within the VMC noise. the profile should match the LDA density, which is also shown. Assuming that the LDA density is reasonably accurate, this provides a reference for the results to follow. First, the effect of introducing only the homogeneous short-ranged two-body term u cusp is investigated. Fahy and coworkers [21] were the first to point out in the context of quantum Monte Carlo simulations that adding a homogeneous 11 twobody term causes the electron density to become more uniform; this is seen in figure 8.15. However, the effect is small. The change in electron density brought about by using the plasmon two-body term is much more dramatic, and is illustrated in figure 8.16. The long-range correlations cause the electron density to be pushed almost entirely into bands outside 11 The term ‘homogeneous’ here refers to the fact that u only depends on the relative spin and separation of the electrons, and not on their individual positions. 156
CHAPTER 8. APPLYING THE PLASMON NORMAL MODE THEORY TO SLAB SYSTEMS 0.06 LDA u cusp n(z) 0.04 0.02 0 0 s z Figure 8.15: The effect on the electron density of including a homogeneous two-body term of the form given in equation (8.113) in the wave function. The density becomes slightly more homogeneous, with more electrons being pushed into the vacuum regions outside the slab. the original slab. In these regions, u pl is much weaker than in the centre. The function of the one-body term is to restore the correct electron density. Remarkably, given the dramatic separation observed in figure 8.16, this is achieved by χ pl ; figure 8.17 shows the density profile for the full wave function given in equation (8.121). An important test for the plasmonic wave function is to compare it with a wave function containing only the short-range electron-electron cusp terms, u cusp and χ cusp . The density is plotted in figure 8.18, from which it is evident that the original LDA density is almost exactly recovered. This is an indication that the expression (8.119) for χ cusp , which was not rigorously derived but constructed based on a plausibility argument, works very well for this system. The results for a larger system of 1600 electrons are almost identical to those for the 600-electron system; table 8.2 shows the effect of the different Jastrow factors 157
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Improving the accuracy of surface s
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Acknowledgements I am greatly indeb
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CONTENTS 3.3.4 Importance-sampled d
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CONTENTS 10 Conclusions 181 A The q
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LIST OF FIGURES 5.3 The LDA energy
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LIST OF FIGURES 8.4 The x- and z-co
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LIST OF FIGURES 8.20 Electron densi
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List of Tables 8.1 The function F k
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Chapter 1 Introduction In recent de
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CHAPTER 1. INTRODUCTION A successfu
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CHAPTER 2. MECHANICS THE SIMPLIFICA
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CHAPTER 3. QUANTUM MONTE CARLO METH
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Chapter 4 Errors in QMC simulations
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CHAPTER 4. ERRORS IN QMC SIMULATION
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CHAPTER 5. THE JELLIUM SLAB The jel
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CHAPTER 5. THE JELLIUM SLAB 0.08 0.
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CHAPTER 5. THE JELLIUM SLAB The DMC
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CHAPTER 5. THE JELLIUM SLAB -9.125
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CHAPTER 5. THE JELLIUM SLAB -0.3 Su
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CHAPTER 5. THE JELLIUM SLAB 0.14 be
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CHAPTER 5. THE JELLIUM SLAB At the
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CHAPTER 6. THE MODIFIED PERIODIC CO
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Bibliography [1] P. H. Acioli and D
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BIBLIOGRAPHY [19] A. G. Eguiluz and
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BIBLIOGRAPHY [39] P. R. C. Kent, R.
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BIBLIOGRAPHY [59] H. J. Monkhorst a
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BIBLIOGRAPHY [80] C. J. Umrigar, K.
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My PhD thesis - Condensed Matter Theory - Imperial College London

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