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

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

Label
Interacting electrons : theory and computational approaches
Title
Interacting electrons
Title remainder
theory and computational approaches
Statement of responsibility
Richard M. Martin, University of Illinois, Urbana-Champaign, Lucia Reining, Ecole Polytechnique, Palaiseau, David M. Ceperle, University of Illinois, Urbana-Champaign
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Author
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Language
eng
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"--
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1942-
http://library.link/vocab/creatorName
Martin, Richard M.
Illustrations
illustrations
Index
no index present
LC call number
QC176.8.E4
LC item number
M368 2016
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Reining, Lucia
  • Ceperley, David
  • Cambridge University Press
http://library.link/vocab/subjectName
  • Electronic structure
  • Electrons
  • Many-body problem
  • Perturbation (Quantum dynamics)
  • Quantum theory
  • Monte Carlo method
Label
Interacting electrons : theory and computational approaches, Richard M. Martin, University of Illinois, Urbana-Champaign, Lucia Reining, Ecole Polytechnique, Palaiseau, David M. Ceperle, University of Illinois, Urbana-Champaign
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Publication
Bibliography note
Includes bibliographical references and index
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online resource
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cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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 -- 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 -- 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 -- 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 E -- 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 -- 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 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 -- 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 -- 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 -- 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 -- 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: Fe and Ni -- 20.5.Transition metal oxides: overview -- 20.6.Vanadium compounds and metal-insulator transitions -- 20.7.NiO - charge-transfer insulator, antiferromagnetism, and doping -- 20.8.MnO - metal-insulator and spin transitions -- 20.9.Wrap-up -- Select Further Reading -- Exercises -- 21.Combining Green's functions approaches: an outlook -- Summary -- 21.1.Taking advantage of different Green's function methods -- 21.2.Partitioning the system -- 21.3.Combining different levels of diagrammatic approaches -- 21.4.Combining Green's function methods: GW and DMFT -- 21.5.Dynamical interactions and constrained RPA -- 21.6.Consequences of dynamical interactions -- 21.7.Diagrammatic extensions: dynamical vertex approximation and dual fermions -- 21.8.Wrap-up -- Select Further Reading -- Exercises -- 22.Introduction to stochastic methods --
  • Contents note continued: Summary -- 22.1.Simulations -- 22.2.Random walks and Markov chains -- 22.3.The Metropolis Monte Carlo method -- 22.4.Computing error bars -- 22.5.The "heat bath" algorithm -- 22.6.Remarks -- Select Further Reading -- Exercises -- 23.Variational Monte Carlo -- Summary -- 23.1.Details of the variational Monte Carlo method -- 23.2.Optimizing trial wavefunctions -- 23.3.The momentum distribution and single-particle density matrix -- 23.4.Non-local pseudopotentials -- 23.5.Finite-size effects -- 23.6.VMC for lattice models -- 23.7.Excitations and orthogonality -- 23.8.Strengths and weaknesses of VMC -- Select Further Reading -- Exercises -- 24.Projector quantum Monte Carlo -- Summary -- 24.1.Types and properties of projectors -- 24.2.The diffusion Monte Carlo method -- 24.3.Exact fermion methods: the sign or phase problem -- 24.4.The fixed-node and fixed-phase methods -- 24.5.Mixed estimators, exact estimators, and the overlap -- 24.6.Non-local pseudopotentials in PMC -- 24.7.Projector auxiliary-field quantum Monte Carlo methods -- 24.8.Applications of projector MC -- 24.9.The pluses and minuses of projector MC -- Select Further Reading -- Exercises -- 25.Path-integral Monte Carlo -- Summary -- 25.1.The path-integral representation -- 25.2.Exchange of localized electrons -- 25.3.Quantum statistics and PIMC -- 25.4.Ground-state path integrals (GSPI) -- 25.5.Finite-temperature QMC for the Hubbard model -- 25.6.Estimating real-time correlation functions -- 25.7.Correlation-function QMC for excitations -- Select Further Reading -- Exercises -- 26.Concluding remarks -- Appendix A Second quantization -- Summary -- A.1.First quantization -- A.2.Second quantization -- Select Further Reading -- Appendix B Pictures -- Summary -- B.1.Schrödinger picture -- B.2.Heisenberg picture -- B.3.Interaction picture -- Select Further Reading -- Exercises -- Appendix C Green's functions: general properties -- Summary -- C.1.Green's functions for differential equations -- C.2.Fourier transforms and spectral representations -- C.3.Frequency integrals -- C.4.From many-body to few-body Green's functions -- C.5.The thermodynamic limit -- Select Further Reading -- Exercises -- Appendix D Matsubara formulation for Green's functions for Tnot=to0 -- Summary -- D.1.Green's functions at Tnot=to 0: Matsubara frequencies -- D.2.Analytic properties in the complex-frequency plane -- D.3.Illustration of the structure of G°(iwn) and G°(τ) -- D.4.The grand potential Ω -- D.5.Transformation to real frequencies -- Select Further Reading -- Exercises -- Appendix E Time ordering, contours, and non-equilibrium -- Summary -- E.1.The task -- E.2.The contour interpretation -- E.3.Contours for all purposes -- Select Further Reading -- Appendix F Hedin's equations in a basis -- Summary -- F.1.Generalization of Hedin's equations -- F.2.Hedin's equations in a basis -- Select Further Reading -- Appendix G Unique solutions in Green's function theory -- Summary -- G.1.Which G°? Boundary conditions in time -- G.2.Which G? Self-consistent Dyson equations -- G.3.Convergence of perturbation expansions and consequences -- Select Further Reading -- Exercises -- Appendix H Properties of functionals -- Summary -- H.1.Functionals and functional equations -- H.2.Legendre transformations and invertibility -- H.3.Examples of functionals for the total energy in Kohn-Sham DFT calculations -- H.4.Free-energy functionals for spin systems and proof of invertibility -- H.5.Extension to quantum spins and density functional theory -- Select Further Reading -- Exercises -- Appendix I Auxiliary systems and constrained search -- Summary -- I.1.Auxiliary system to reproduce selected quantities -- I.2.Constrained search with an interacting auxiliary system -- Exercises -- Appendix J Derivation of the Luttinger theorem -- Summary -- Select Further Reading -- Exercises -- Appendix K Gutzwiller and Hubbard approaches -- Summary -- K.1.Gutzwiller approach in terms of the wavefunction -- K.2.Hubbard approach in terms of the Green's function -- K.3.Two scenarios for the Mott transition -- Select Further Reading -- Exercises
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unknown
Extent
1 online resource (xiv, 818 pages)
Form of item
online
Isbn
9781139050807
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
99977437838
System control number
(NhCcYBP)13034084
Label
Interacting electrons : theory and computational approaches, Richard M. Martin, University of Illinois, Urbana-Champaign, Lucia Reining, Ecole Polytechnique, Palaiseau, David M. Ceperle, University of Illinois, Urbana-Champaign
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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 -- 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 -- 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 -- 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 E -- 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 -- 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 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 -- 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 -- 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 -- 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 -- 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: Fe and Ni -- 20.5.Transition metal oxides: overview -- 20.6.Vanadium compounds and metal-insulator transitions -- 20.7.NiO - charge-transfer insulator, antiferromagnetism, and doping -- 20.8.MnO - metal-insulator and spin transitions -- 20.9.Wrap-up -- Select Further Reading -- Exercises -- 21.Combining Green's functions approaches: an outlook -- Summary -- 21.1.Taking advantage of different Green's function methods -- 21.2.Partitioning the system -- 21.3.Combining different levels of diagrammatic approaches -- 21.4.Combining Green's function methods: GW and DMFT -- 21.5.Dynamical interactions and constrained RPA -- 21.6.Consequences of dynamical interactions -- 21.7.Diagrammatic extensions: dynamical vertex approximation and dual fermions -- 21.8.Wrap-up -- Select Further Reading -- Exercises -- 22.Introduction to stochastic methods --
  • Contents note continued: Summary -- 22.1.Simulations -- 22.2.Random walks and Markov chains -- 22.3.The Metropolis Monte Carlo method -- 22.4.Computing error bars -- 22.5.The "heat bath" algorithm -- 22.6.Remarks -- Select Further Reading -- Exercises -- 23.Variational Monte Carlo -- Summary -- 23.1.Details of the variational Monte Carlo method -- 23.2.Optimizing trial wavefunctions -- 23.3.The momentum distribution and single-particle density matrix -- 23.4.Non-local pseudopotentials -- 23.5.Finite-size effects -- 23.6.VMC for lattice models -- 23.7.Excitations and orthogonality -- 23.8.Strengths and weaknesses of VMC -- Select Further Reading -- Exercises -- 24.Projector quantum Monte Carlo -- Summary -- 24.1.Types and properties of projectors -- 24.2.The diffusion Monte Carlo method -- 24.3.Exact fermion methods: the sign or phase problem -- 24.4.The fixed-node and fixed-phase methods -- 24.5.Mixed estimators, exact estimators, and the overlap -- 24.6.Non-local pseudopotentials in PMC -- 24.7.Projector auxiliary-field quantum Monte Carlo methods -- 24.8.Applications of projector MC -- 24.9.The pluses and minuses of projector MC -- Select Further Reading -- Exercises -- 25.Path-integral Monte Carlo -- Summary -- 25.1.The path-integral representation -- 25.2.Exchange of localized electrons -- 25.3.Quantum statistics and PIMC -- 25.4.Ground-state path integrals (GSPI) -- 25.5.Finite-temperature QMC for the Hubbard model -- 25.6.Estimating real-time correlation functions -- 25.7.Correlation-function QMC for excitations -- Select Further Reading -- Exercises -- 26.Concluding remarks -- Appendix A Second quantization -- Summary -- A.1.First quantization -- A.2.Second quantization -- Select Further Reading -- Appendix B Pictures -- Summary -- B.1.Schrödinger picture -- B.2.Heisenberg picture -- B.3.Interaction picture -- Select Further Reading -- Exercises -- Appendix C Green's functions: general properties -- Summary -- C.1.Green's functions for differential equations -- C.2.Fourier transforms and spectral representations -- C.3.Frequency integrals -- C.4.From many-body to few-body Green's functions -- C.5.The thermodynamic limit -- Select Further Reading -- Exercises -- Appendix D Matsubara formulation for Green's functions for Tnot=to0 -- Summary -- D.1.Green's functions at Tnot=to 0: Matsubara frequencies -- D.2.Analytic properties in the complex-frequency plane -- D.3.Illustration of the structure of G°(iwn) and G°(τ) -- D.4.The grand potential Ω -- D.5.Transformation to real frequencies -- Select Further Reading -- Exercises -- Appendix E Time ordering, contours, and non-equilibrium -- Summary -- E.1.The task -- E.2.The contour interpretation -- E.3.Contours for all purposes -- Select Further Reading -- Appendix F Hedin's equations in a basis -- Summary -- F.1.Generalization of Hedin's equations -- F.2.Hedin's equations in a basis -- Select Further Reading -- Appendix G Unique solutions in Green's function theory -- Summary -- G.1.Which G°? Boundary conditions in time -- G.2.Which G? Self-consistent Dyson equations -- G.3.Convergence of perturbation expansions and consequences -- Select Further Reading -- Exercises -- Appendix H Properties of functionals -- Summary -- H.1.Functionals and functional equations -- H.2.Legendre transformations and invertibility -- H.3.Examples of functionals for the total energy in Kohn-Sham DFT calculations -- H.4.Free-energy functionals for spin systems and proof of invertibility -- H.5.Extension to quantum spins and density functional theory -- Select Further Reading -- Exercises -- Appendix I Auxiliary systems and constrained search -- Summary -- I.1.Auxiliary system to reproduce selected quantities -- I.2.Constrained search with an interacting auxiliary system -- Exercises -- Appendix J Derivation of the Luttinger theorem -- Summary -- Select Further Reading -- Exercises -- Appendix K Gutzwiller and Hubbard approaches -- Summary -- K.1.Gutzwiller approach in terms of the wavefunction -- K.2.Hubbard approach in terms of the Green's function -- K.3.Two scenarios for the Mott transition -- Select Further Reading -- Exercises
Dimensions
unknown
Extent
1 online resource (xiv, 818 pages)
Form of item
online
Isbn
9781139050807
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
99977437838
System control number
(NhCcYBP)13034084

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