Interacting electrons : theory and computational approaches / Richard M. Martin, University of Illinois, Urbana-Champaign, Lucia Reining, Ecole Polytechnique, Palaiseau, David M. Ceperley, University of Illinois, Urbana-Champaign.

Format:

Book

Author/Creator:

Martin, Richard M., 1942- author.

Reining, Lucia, author.

Ceperley, David, author.

Contributor:

Carl Hering Library Fund.

Language:

English

Subjects (All):

Electronic structure.

Electrons.

Many-body problem.

Perturbation (Quantum dynamics).

Quantum theory.

Monte Carlo method.

Physical Description:

xiv, 818 pages : illustrations ; 26 cm

Place of Publication:

New York, NY : Cambridge University Press, 2016.

Summary:

"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"-- Provided by publisher.

Contents:

Machine generated contents note: 1. The many-electron problem: introduction

Summary

1.1. The electronic structure problem

1.2. Why is this problem hard?

1.3. Why is the independent-electron picture so successful?

1.4. Development of theoretical approaches to the many-body problem

1.5. The many-body problem and computation

1.6. The scope of this book

Select Further Reading

2. Signatures of electron correlation

2.1. What is meant by correlation?

2.2. Ground-state and thermodynamic properties

2.3. Magnetism and local moments

2.4. Electron addition and removal: the bandgap problem and more

2.5. Satellites and sidebands

2.6. Particle-hole and collective excitations

2.7. The Kondo effect and heavy fermions

2.8. Mott insulators and metal-insulator transitions

2.9. Lower dimensions: stronger interaction effects

2.10. Wrap-up

3 Concepts and models for interacting electrons

3.1. The Wigner transition and the homogeneous electron system

3.2. The Mott transition and the Hubbard model

3.3. Magnetism and spin models

3.4. Normal metals and Fermi liquid theory

3.5. The Kondo effect and the Anderson impurity model

3.6. The Luttinger theorem and the Friedel sum rule

Exercises

4. Mean fields and auxiliary systems

4.1. The Hartree and Hartree-Fock approximations

4.2. Weiss mean field and the Curie-Weiss approximation

4.3. Density functional theory and the Kohn-Sham auxiliary system

4.4. The Kohn-Sham electronic structure

4.5. Extensions of the Kohn-Sham approach

4.6. Time-dependent density and current density functional theory

4.7. Symmetry breaking in mean-field approximations and beyond

4.8. Wrap-up

5 Correlation functions

5.1. Expectation values and correlation functions

5.2. Static one-electron properties

5.3. Static two-particle correlations: density correlations and the structure factor

5.4. Dynamic correlation functions

5.5. Response functions

5.6. The one-particle Green's function

5.7. Useful quantities derived from the one-particle Green's function

5.8. Two-particle Green's functions

6. Many-body wavefunctions

6.1. Properties of the many-body wavefunction

6.2. Boundary conditions

6.3. The ground-state wavefunction of insulators

6.4. Correlation in two-electron systems

6.5. Trial function local energy, Feynman-Kac formula, and wavefunction quality

6.6. The pair product or Slater-Jastrow wavefunction

6.7. Beyond Slater determinants

7. Particles and quasi-particles$g5 Summary

7.1. Dynamical equations and Green's functions for coupled systems

7.2. The self-energy and the Dyson equation

7.3. Illustration: a single state coupled to a continuum

7.4. Interacting systems: the self-energy and spectral function

7.5. Quasi-particles

7.6. Quasi-particle equations

7.7. Separating different contributions to a Dyson equation

7.8. Wrap-up

8. Functionals in many-particle physics

8.1. Density functional theory and the Hartree-Fock approximation

8.2. Functionals of the Green's function G and self-energy E

8.3. Functionals of the screened interaction W

8.4. Generating functionals

8.5. Conservation laws and conserving approximations

8.6. Wrap-up

9. Many-body perturbation theory: expansion in the interaction

9.1d quasi-particles$g5 The Coulomb interaction and perturbation theory

9.2. Connecting the interacting and non-interacting systems

9.3. Telling the story of particles: diagrams

9.4. Making the story easier: two theorems

9.5. Dyson equation for the one-particle Green's function, and the self-energy

9.6. Diagrammatic expansion at non-vanishing temperature

9.7. Self-consistent perturbation theory: from bare to dressed building blocks

9.8. The Luttinger-Ward functional

9.9. Wrap-up

10. Many-body perturbation theory via functional derivatives

10.1. The equation of motion

10.2. The functional derivative approach

10.3. Dyson equations

10.4. Conservation laws

10.5. A starting point for approximations

10.6. Wrap-up

11. The RPA and the GW approximation for the self-energy

11.1s$g5 Hedin's equations

11.2. Neglecting vertex corrections in the polarizability: the RPA

11.3. Neglecting vertex corrections in the self-energy: the GW approximation

11.4. Link between the GWA and static mean-field approaches

11.5. Ground-state properties from the GWA

11.6. The GWA in the homogeneous electron gas

11.7. The GWA in small model systems

11.8. Wrap-up

12. GWA calculations in practice

12.1. The task: a summary

12.2. Frequently used approximations

12.3. Core and valence

12.4. Different levels of self-consistency

12.5. Frequency integrations

12.6. GW calculations in a basis

12.7. Scaling and convergence

12.8. Wrap-up

13. GWA calculations: illustrative results

13.1. From the HEG to a real semiconductor: silicon as a prototype system

13.2 Materials properties in the GWA: an overview

13.3. Energy levels in finite and low-dimensional systems

13.4. Transition metals and their oxides

13.5. GW results for the ground state

13.6. A comment on temperature

13.7. Wrap-up

14. RPA and beyond: the Bethe-Salpeter equation

14.1. The two-particle correlation function and measurable quantities

14.2. The two-particle correlation function: basic relations

14.3. The RPA: what can it yield?

14.4. Beyond the RPA: spin and frequency structure of the BSE

14.5. The Bethe-Salpeter equation in the GW approximation

14.6. A two-body Schrödinger equation

14.7. Importance and analysis of electron-hole interaction effects

14.8. Bethe-Salpeter calculations in practice

14.9. Applications

14.10. Extensions

14.11. Linear response using Green's functions or density functionals 14.12. Wrap-up

15. Beyond the GW approximation

15.1. The need to go beyond GW: analysis and observations

15.2. Iterating Hedin's equations

15.3. Effects of vertex corrections

15.4. The T-matrix and related approximations

15.5. Beyond the T-matrix approximation: combining channels

15.6. T-matrix and related approaches in practice

15.7. Cumulants in electron spectroscopy

15.8. Use of exact constraints

15.9. Retrospective and outlook

16. Dynamical mean-field theory

16.1. Auxiliary systems and embedding in Green's function methods

16.2. Overview of DMFT

16.3. Expansion around an atomic limit: low energy scales and strong temperature dependence

16.4. Background for mean-field theories and auxiliary systems

16.5. Dynamical mean-field equations

16.6unctionals Self-energy functional and variational equations

16.7. Static properties and density matrix embedding

16.8. Single-site DMFA in a two-site model

16.9. The Mott transition in infinite dimensions

16.10. Hybridized bands and consequences for the Mott transition

16.11. Interacting

Bands and spin transitions

16.12. Wrap-up

17. Beyond the single-site approximation in DMFT

17.1. Supercells and clusters

17.2. Cellular DMFA

17.3. Dynamic cluster approximation

17.4. Variational cluster and nested cluster approximations

17.5. Extended DMFT and auxiliary bosons

17.6. Results for Hubbard models in one, two, and three dimensions

17.7. Wrap-up

18. Solvers for embedded systems

18.1. The problem(s) to be solved

18.2. Exact diagonalization and related methods

18.3^s^^^ Path-integral formulation in terms of the action

18.4. Auxiliary-field methods and the Hirsch-Fye algorithm

18.5. CTQMC: expansion in the interaction

18.6. CTQMC: expansion in the hybridization

18.7. Dynamical interactions in CTQMC

18.8. Other methods

18.9. Wrap-up

19. Characteristic hamiltonians for solids with d and f states

19.1. Transition elements: atomic-like behavior and local moments

19.2. Hamiltonian in a localized basis: crystal fields, bands, Mott-Hubbard vs. charge transfer

19.3. Effective interaction hamiltonian

19.4. Identification of localized orbitals

19.5. Combining DMFT and DFT

19.6. Static mean-field approximations: DFT+U, etc.

19.7. Wrap-up

20. Examples of calculations for solids with d and f states

20.1^zation and related methods

18.3^s^^^ Kondo effect in realistic multi-orbital problems

20.2. Lanthanides

magnetism, volume collapse, heavy fermions, mixed valence, etc.

20.3. Actinides

transition from band to localized

20.4. Transition metals

local moments and ferromagnetism

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Carl Hering Library Fund.

ISBN:

9780521871501

0521871506

OCLC:

930462965