My PhD thesis - Condensed Matter Theory - Imperial College London

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CHAPTER 3. QUANTUM MONTE CARLO METHODS and regenerate the configurations once the minimum has been found. Despite the difficulties involved in these schemes, they are far more efficient than regenerating configurations for each set of parameters. Variance minimisation is not infallible, and several alternatives have been proposed; these include different optimisation functionals [2, 11] or the method of stochastic gradients [31]. 56
Chapter 4 Errors in QMC simulations This chapter will describe the most significant errors inherent in extended-system QMC simulations. Two of these — statistical noise and the fixed-node error — have already been mentioned in the previous chapter; when attempting to simulate extended systems, finite-size errors also become important. 1 4.1 Finite-size errors The QMC methods described in Chapter 3 apply to finite systems. To investigate the properties of materials which have infinite extent in at least one spatial dimension, some kind of scheme for extrapolation is required. In practice, such materials are studied by placing a finite set of particles in a simulation cell, which is then subjected to periodic boundary conditions. This defines a lattice (see figure 4.1). To complicate things, the particles must also undergo interactions with their periodically-repeated images; the best way to take account of this is not obvious. In this report, the particles will be exclusively electrons, interacting via the Coulomb force, the long-ranged nature of which is a key part of the problem. 1 The use of pseudopotentials introduces additional errors in the simulation of real atoms, but these will not be discussed in this work. 57
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Improving the accuracy of surface s
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Acknowledgements I am greatly indeb
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Page 7 and 8: CONTENTS 10 Conclusions 181 A The q
Page 9 and 10: LIST OF FIGURES 5.3 The LDA energy
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CHAPTER 7. THE ELECTRONIC GROUND-ST
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CHAPTER 8. APPLYING THE PLASMON NOR
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CHAPTER 9. ENERGY A NEW CALCULATION
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Chapter 10 Conclusions The original
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CHAPTER 10. CONCLUSIONS pling and o
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APPENDIX A. THE QUASI-2D EWALD SUM
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APPENDIX B. THE CUSP CONDITIONS may
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APPENDIX B. THE CUSP CONDITIONS wit
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APPENDIX C. INTEGRATING THE CUSP FU
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APPENDIX C. INTEGRATING THE CUSP FU
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APPENDIX D. RECONSTRUCTING A PROBAB
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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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