Martin R.M., Reining L., Ceperley D.M. Interacting Electrons: Theory and Computational Approaches

Cambridge University Press, UK, 2016. — 843 p. — ISBN: 0521871506Recent 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.Interacting electrons: beyond the independent-particle picture
The many-electron problem: introduction
Signatures of electron correlation
Concepts and models for interacting electrons
Foundations of theory for many-body systems
Mean fields and auxiliary systems
Correlation functions
Many-body wavefunctions
Particles and quasi-particles
Functionals in many-particle physics
Many-body Green’s function methods
9 Many-body perturbation theory: expansion in the interaction
10 Many-body perturbation theory via functional derivatives
The RPA and the GW approximation for the self-energy
GWA calculations in practice
GWA calculations: illustrative results
RPA and beyond: the Bethe–Salpeter equation
Beyond the GW approximation
Dynamical mean-field theory
Beyond the single-site approximation in DMFT
Solvers for embedded systems
Characteristic hamiltonians for solids with d and f states
Examples of calculations for solids with d and f states
Combining Green’s functions approaches: an outlook
Stochastic methods
Introduction to stochastic methods
Variational Monte Carlo
Projector quantum Monte Carlo
Path-integral Monte Carlo
Concluding remarks
Appendices
Second quantization
Pictures
Green’s functions: general properties
Matsubara formulation for Green’s functions for T /= 0
Time ordering, contours, and non-equilibrium
Hedin’s equations in a basis
Unique solutions in Green’s function theory
Properties of functionals
Auxiliary systems and constrained search
Derivation of the Luttinger theorem
Gutzwiller and Hubbard approaches