Richard M. Martin, Lucia Reining, David M. CeperleyCambridge University Press, 6/30/2016EAN 9780521871501, ISBN10: 0521871506Hardcover, 840 pages, 25.3 x 18.3 x 4.1 cmLanguage: EnglishRecent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.PrefacePart I. Interacting ElectronsBeyond the Independent-Particle Picture1. The many electron problemintroduction2. Signatures of electron correlation3. Concepts and models for interacting electronsPart II. Foundations of Theory for Many-Body Systems4. Mean fields and auxiliary systems5. Correlation functions6. Many-body wavefunctions7. Particles and quasi-particles8. Functionals in many-particle physicsPart III. Many-Body Green's Function Methods9. Many-body perturbation theoryexpansion in the interaction10. Many-body perturbation theory via functional derivatives11. The RPA and the GW approximation for the self-energy12. GWA calculations in practice13. GWA calculationsillustrative results14. RPA and beyondthe Bethe-Salpeter equation15. Beyond the GW approximation16. Dynamical mean field theory17. Beyond the single-site approximation in DMFT18. Solvers for embedded systems19. Characteristic hamiltonians for solids with d and f states20. Examples of calculations for solids with d and f states21. Combining Green's functions approachesan outlookPart IV. Stochastic Methods22. Introduction to stochastic methods23. Variational Monte Carlo24. Projector quantum Monte Carlo25. Path integral Monte Carlo26. Concluding remarksPart V. AppendicesA. Second quantizationB. PicturesC. Green's functionsgeneral propertiesD. Matsubara formulation for Green's functions for T ̸= 0E. Time-ordering, contours, and non-equilibriumF. Hedin's equations in a basisG. Unique solutions in Green's function theoryH. Properties of functionalsI. Auxiliary systems and constrained searchJ. Derivation of the Luttinger theoremK. Gutzwiller and Hubbard approachesReferencesIndex.
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