UID:
almafu_9960116992602883
Format:
1 online resource (xxiv, 818 pages) :
,
digital, PDF file(s).
ISBN:
1-316-55739-1
,
1-316-56012-0
,
1-139-05080-X
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 06 Jun 2016).
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Cover -- Half-title page -- Title page -- Copyright page -- Dedication -- Contents -- Preface -- Acknowledgments -- Notation -- Part I Interacting electrons: beyond the independent-particle picture -- 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 -- Summary -- 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 -- Summary -- 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 -- Select further reading -- Exercises -- Part II Foundations of theory for many-body systems -- 4 Mean fields and auxiliary systems -- Summary -- 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.
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4.6 Time-dependent density and current density functional theory -- 4.7 Symmetry breaking in mean-field approximations and beyond -- 4.8 Wrap-up -- Select further reading -- Exercises -- 5 Correlation functions -- Summary -- 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 -- Select further reading -- Exercises -- 6 Many-body wavefunctions -- Summary -- 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 -- Exercises -- 7 Particles and quasi-particles -- 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 -- Select further reading -- Exercises -- 8 Functionals in many-particle physics -- Summary -- 8.1 Density functional theory and the Hartree-Fock approximation -- 8.2 Functionals of the Green's function G and self-energy -- 8.3 Functionals of the screened interaction W -- 8.4 Generating functionals -- 8.5 Conservation laws and conserving approximations -- 8.6 Wrap-up -- Select further reading -- Exercises.
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Part III Many-body Green's function methods -- 9 Many-body perturbation theory: expansion in the interaction -- Summary -- 9.1 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 theself-energy -- 9.6 Diagrammatic expansion at non-vanishing temperature -- 9.7 Self-consistent perturbation theory: from bare to dressed buildingblocks -- 9.8 The Luttinger-Ward functional -- 9.9 Wrap-up -- Select further reading -- Exercises -- 10 Many-body perturbation theory via functional derivatives -- Summary -- 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 -- Select further reading -- Exercises -- 11 The RPA and the GW approximation for the self-energy -- Summary -- 11.1 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 -- Select further reading -- Exercises -- 12 GWA calculations in practice -- Summary -- 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 -- Select further reading -- Exercises -- 13 GWA calculations: illustrative results -- Summary.
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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 -- Select further reading -- Exercises -- 14 RPA and beyond: the Bethe-Salpeter equation -- Summary -- 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 -- Select further reading -- Exercises -- 15 Beyond the GW approximation -- Summary -- 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 -- Select further reading -- Exercises -- 16 Dynamical mean-field theory -- Summary -- 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.
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16.6 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 -- Select further reading -- Exercises -- 17 Beyond the single-site approximation in DMFT -- Summary -- 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 -- Select further reading -- Exercises -- 18 Solvers for embedded systems -- Summary -- 18.1 The problem(s) to be solved -- 18.2 Exact diagonalization and related methods -- 18.3 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 -- Select further reading -- Exercises -- 19 Characteristic hamiltonians for solids with d and f states -- Summary -- 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 -- Select further reading -- Exercises -- 20 Examples of calculations for solids with d and f states -- Summary -- 20.1 Kondo effect in realistic multi-orbital problems.
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20.2 Lanthanides - magnetism, volume collapse, heavy fermions, mixed valence, etc.
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English
Additional Edition:
ISBN 0-521-87150-6
Language:
English
Subjects:
Physics
URL:
https://doi.org/10.1017/CBO9781139050807
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