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Interacting Electrons
Theory and Computational Approaches


  • Date Published: June 2016
  • availability: In stock
  • format: Hardback
  • isbn: 9780521871501

$ 84.99

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About the Authors
  • 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
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    Product details

    • Date Published: June 2016
    • format: Hardback
    • isbn: 9780521871501
    • length: 840 pages
    • dimensions: 253 x 183 x 41 mm
    • weight: 1.76kg
    • contains: 203 b/w illus. 5 tables 203 exercises
    • availability: In stock
  • Table of Contents

    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

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    Interacting Electrons

    Richard M. Martin, Lucia Reining, David M. Ceperley

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  • Authors

    Richard M. Martin, University of Illinois, Urbana-Champaign
    Richard M. Martin is Emeritus Professor at the University of Illinois, Urbana-Champaign, and Consulting Professor at Stanford University. He has made extensive contributions to the field of modern electronic structure methods and the theory of interacting electron systems and and he is the author of the companion book Electronic Structure: Basic Theory and Methods.

    Lucia Reining, École Polytechnique, Paris
    Lucia Reining is CNRS senior researcher at the Ecole Polytechnique Palaiseau and founding member of the European Theoretical Spectroscopy Facility. Her work covers many-body perturbation theory and time-dependant density functional theory and she is a recipient of the CNRS Silver Medal and a Fellow of the American Physical Society.

    David M. Ceperley, University of Illinois, Urbana-Champaign
    David M. Ceperley is Blue Waters Professor at the University of Illinois, Urbana-Champaign, where he has pioneered the quantum Monte Carlo method, including the development of variational, diffusion and path integral Monte Carlo. He is a member of the US National Academy of Sciences and recipient of the Rahman Prize for Computational Physics of the APS and the Feenberg Medal for many-body physics.

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