My PhD thesis - Condensed Matter Theory - Imperial College London

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Abstract This thesis will address the problem of carrying out electronic structure calculations on quasi-2D systems, focusing on the use of quantum Monte Carlo methods and using the quasi-2D electron gas as a test system. Two techniques aimed at improving the accuracy of these simulations will be proposed and tested: • the use of a modified periodic Coulomb interaction to reduce finite-size errors. It will be shown that the modified interaction does not reduce the finite-size errors; this failure will be analysed and explained. However, it is significantly faster than the conventional interaction, and is therefore recommended. • the application of classical plasmon theory to improve the quality of trial wave functions. A new, intuitive approach to the connection between plasmons and the electronic wave function based on physical arguments will be presented. The predictions for the general form of the wave function in inhomogeneous materials agree with previous results obtained by other methods. In addition, the new approach makes clear the role of classical plasmon normal modes; an analysis of these modes in the case of the quasi-2D electron gas leads directly to an improved wave function for this system. Finally, a new calculation of the surface energy of the electron gas will be presented. 2
Acknowledgements I am greatly indebted to the many people who have helped and supported me in various ways during the course of this degree. My flatmates from Burgoyne Road, my friends from Oxford, my colleagues from the Condensed Matter Theory group, my teammates from Brixton Town and my fellow Beards have all contributed to keeping me happy over the last three years. I have been very lucky to have a supervisor as enthusiastic, dedicated and supportive as Matthew Foulkes, who has taught me a great deal. Finally, I am incredibly grateful to Debora, Emma and my parents for their wonderful love and support. 3
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CHAPTER 3. QUANTUM MONTE CARLO METH
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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 0.14 be
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CHAPTER 5. THE JELLIUM SLAB At the
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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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