Interacting Electrons
Theory and Computational Approaches

This book sets out modern methods of computing properties of materials, including essential theoretical background, computational approaches, practical guidelines and instructive applications.

Richard M. Martin (Author), Lucia Reining (Author), David M. Ceperley (Author)

9780521871501, Cambridge University Press

Hardback, published 30 June 2016

840 pages, 203 b/w illus. 5 tables 203 exercises
25.3 x 18.3 x 4.1 cm, 1.76 kg

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.

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.

Subject Areas: Computer science [UY], Computing & information technology [U], Condensed matter physics [liquid state & solid state physics PHFC], Materials / States of matter [PHF], Mathematics & science [P]