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Interacting Electrons: Theory and Computational Approaches

Interacting Electrons: Theory and Computational Approaches
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Dewey Class 539.7 (DDC 23)
Title Interacting Electrons (M) : Theory and Computational Approaches / Richard M. Martin, Lucia Reining and David M. Ceperley
Author Martin, Richard M. , 1942-
Added Personal Name Reining, Lucia
Ceperley, David
Publication Cambridge, U.K. : Cambridge University Press , 2016
Physical Details xxiv, 818 pages : illustrations ; 26 cm.
ISBN 9780521871501
Note Recent 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. Provides extensive background and theory for each of the methods, which enables readers to understand capabilities as well as limitations, and how to avoid errors when making computations. Designed to be accessible for beginners with non-technical introductory chapters for each method. Chapters are complemented with exercises enabling students to master the theory by putting the tools to practical use.
Online publication date:June 2016
Contents note Preface Part I. Interacting Electrons: Beyond the Independent-Particle Picture:1. The many electron problem: introduction 2. Signatures of electron correlation 3. Concepts and models for interacting electrons Part II. Foundations of Theory for Many-Body Systems: 4. Mean fields and auxiliary systems 5. Correlation functions 6. Many-body wavefunctions 7. Particles and quasi-particles 8. Functionals in many-particle physics Part III. Many-Body Green's Function Methods: 9. Many-body perturbation theory: expansion in the interaction 10. Many-body perturbation theory via functional derivatives 11. The RPA and the GW approximation for the self-energy 12. GWA calculations in practice 13. GWA calculations: illustrative results 14. RPA and beyond: the Bethe-Salpeter equation 15. Beyond the GW approximation 16. Dynamical mean field theory 17. Beyond the single-site approximation in DMFT 18. Solvers for embedded systems 19. Characteristic hamiltonians for solids with d and f states 20. Examples of calculations for solids with d and f states 21. Combining Green's functions approaches: an outlook Part IV. Stochastic Methods: 22. Introduction to stochastic methods 23. Variational Monte Carlo 24. Projector quantum Monte Carlo 25. Path integral Monte Carlo 26. Concluding remarks Part V. Appendices: A. Second quantization B. Pictures C. Green's functions: general properties D. Matsubara formulation for Green's functions for T ̸= 0 E. Time-ordering, contours, and non-equilibrium F. Hedin's equations in a basis G. Unique solutions in Green's function theory H. Properties of functionals I. Auxiliary systems and constrained search J. Derivation of the Luttinger theorem K. Gutzwiller and Hubbard approaches References Index.
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