Interacting Electrons Theory and Computational Approaches 1st Edition by Richard M Martin,Lucia Reining,David M Ceperley ISBN 0521871506 978-0521871501

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Product details:

ISBN 10: 0521871506 

ISBN 13: 978-0521871501

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

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.

Table of contents:

Part I – Interacting Electrons: Beyond the Independent-Particle Picture

Chapter 1 – The Many-Electron Problem: Introduction

Chapter 2 – Signatures of Electron Correlation

Chapter 3 – Concepts and Models for Interacting Electrons

Part II – Foundations of Theory for Many-Body Systems

Chapter 4 – Mean Fields and Auxiliary Systems

Chapter 5 – Correlation Functions

Chapter 6 – Many-Body Wavefunctions

Chapter 7 – Particles and Quasi-Particles

Chapter 8 – Functionals in Many-Particle Physics

Part III – Many-Body Green’s Function Methods

Chapter 9 – Many-Body Perturbation Theory: Expansion in the Interaction

Chapter 10 – Many-Body Perturbation Theory via Functional Derivatives

Chapter 11 – The RPA and the GW Approximation for the Self-Energy

Chapter 12 – GWA Calculations in Practice

Chapter 13 – GWA Calculations: Illustrative Results

Chapter 14 – RPA and Beyond: The Bethe–Salpeter Equation

Chapter 15 – Beyond the GW Approximation

Chapter 16 – Dynamical Mean-Field Theory

Chapter 17 – Beyond the Single-Site Approximation in DMFT

Chapter 18 – Solvers for Embedded Systems

Chapter 19 – Characteristic Hamiltonians for Solids with d and f States

Chapter 20 – Examples of Calculations for Solids with d and f States

Chapter 21 – Combining Green’s Functions Approaches: An Outlook

Part IV – Stochastic Methods

Chapter 22 – Introduction to Stochastic Methods

Chapter 23 – Variational Monte Carlo

Chapter 24 – Projector Quantum Monte Carlo

Chapter 25 – Path-Integral Monte Carlo

Chapter 26 – Concluding Remarks

Part V – Appendices

Appendix A – Second Quantization

Appendix B – Pictures

Appendix C – Green’s Functions: General Properties

Appendix D – Matsubara Formulation for Green’s Functions for T ≠ 0

Appendix E – Time Ordering, Contours, and Non-Equilibrium

Appendix F – Hedin’s Equations in a Basis

Appendix G – Unique Solutions in Green’s Function Theory

Appendix H – Properties of Functionals

Appendix I – Auxiliary Systems and Constrained Search

Appendix J – Derivation of the Luttinger Theorem

Appendix K – Gutzwiller and Hubbard Approaches

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