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Correlated electrons in quantum matter /

by Fulde, Peter [aut].
Material type: materialTypeLabelBookPublisher: Singapore ; Hackensack, NJ : World Scientific, c2012Description: xiii, 535 p. : ill. (some col.) ; 24 cm.ISBN: 9789814390927 (pbk.); 9814390925 (pbk.); 9789814390910 (hbk.); 9814390917 (hbk.).Subject(s): Electron configuration | Solid state physics
Contents:
Preface; Contents; List of Acronyms; 1 Introduction; 2 Independent Electrons; 2.1 Many-Electron Hamiltonian; 2.2 Basis Sets; 2.3 Self-consistent Field Equations; 2.4 Unrestricted SCF Approximation; 2.5 Missing Features of the Independent-Electron Approximation; 3 Homogeneous Electron Gas; 3.1 Uncorrelated Electrons; 3.2 Random-Phase Approximation; 3.3 Wigner Crystal; 4 Density Functional Theory; 4.1 Theory of Hohenberg, Kohn and Sham; 4.2 Local-Density Approximation and Extensions; 4.3 Strong Electron Correlations: LDA+U; 4.4 The Energy Gap Problem; 4.5 Time-Dependent DFT. 5 Wavefunction-Based Methods5.1 Method of Configuration Interactions; 5.2 Cumulants and their Properties; 5.3 Ground-State Wavefunction and Energy; 5.3.1 Method of Increments; 5.4 Different Approximation Schemes.; 5.4.1 Partitioning and Projection Methods; 5.4.2 Coupled Cluster Method; 5.4.3 Selection of Excitation Operators; 5.4.4 Trial Wavefunctions; 6 Correlated Ground-State Wavefunctions; 6.1 Semiconductors; 6.1.1 Model for Interatomic Correlations; 6.1.2 Estimates of Intra-Atomic Correlations; 6.1.3 Ab Initio Results; 6.2 Ionic and van der Waals Solids. 6.2.1 Three Oxides: MgO, CaO and NiO6.2.2 Rare-Gas Solids; 6.3 Simple Metals; 6.4 Ground States with Strong Correlations: CASSCF; 7 Quasiparticle Excitations; 7.1 Single-particle Green's Function; 7.1.1 Perturbation Expansions; 7.1.2 Temperature Green's Function; 7.2 Quasiparticles in Metals; 7.3 Quasiparticles in Semiconductors and Insulators; 7.3.1 Quasiparticle Approximation; 7.3.2 A Simple Model: Bond-Orbital Approximation; 7.3.3 Wavefunction-Based Ab Inito Calculations; 8 Incoherent Excitations; 8.1 Projection Method; 8.2 An Example: Hubbard Model; 9 Coherent-Potential Approximations. 9.1 Static Disorder9.2 Dynamical Disorder: DMFT and Beyond; 10 Strongly Correlated Electrons; 10.1 Measure of Correlation Strengths; 10.2 Indicators of Strong Correlations; 10.2.1 Low-Energy Scales: a Simple Model; 10.2.2 Effective Hamiltonians; 10.3 Kondo Effect; 10.4 The Hubbard Model Revisited; 10.4.1 Spin-Density Wave Ground State; 10.4.2 Gutzwiller's Ground-State Wavefunction; 10.4.3 Hubbard's Approximations and their Extensions; 10.4.4 Kanamori Limit; 10.5 The t-J Model; 10.6 Mean-Field Approximations; 10.6.1 Test of Different Approximation Schemes; 10.7 Metal-Insulator Transitions. 10.8 Numerical Studies10.9 Break-down of Fermi Liquid Description; 10.9.1 Marginal Fermi Liquid Behavior; 10.9.2 Charged and Neutral Quasiparticles; 10.9.3 Hubbard Chains; 10.9.4 Quantum Critical Point; 11 Transition Metals; 11.1 Ground-State Wavefunction; 11.2 Satellite Structures; 11.3 Temperature-Dependent Magnetism; 11.3.1 Local Spin Fluctuations; 11.3.2 Long-Wavelength Spin Fluctuations; 12 Transition-Metal Oxides; 12.1 Doped Charge-Transfer Systems: the Cuprates; 12.1.1 Quasiparticle-like Excitations; 12.2 Orbital Ordering; 12.2.1 Manganites: LaMnOa and related Compounds.
Summary: "It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics."--P. [4] of cover.
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530.41 F962 (Browse shelf) Available

Includes bibliographical references (p. [509]-524) and index.

Preface; Contents; List of Acronyms; 1 Introduction; 2 Independent Electrons; 2.1 Many-Electron Hamiltonian; 2.2 Basis Sets; 2.3 Self-consistent Field Equations; 2.4 Unrestricted SCF Approximation; 2.5 Missing Features of the Independent-Electron Approximation; 3 Homogeneous Electron Gas; 3.1 Uncorrelated Electrons; 3.2 Random-Phase Approximation; 3.3 Wigner Crystal; 4 Density Functional Theory; 4.1 Theory of Hohenberg, Kohn and Sham; 4.2 Local-Density Approximation and Extensions; 4.3 Strong Electron Correlations: LDA+U; 4.4 The Energy Gap Problem; 4.5 Time-Dependent DFT. 5 Wavefunction-Based Methods5.1 Method of Configuration Interactions; 5.2 Cumulants and their Properties; 5.3 Ground-State Wavefunction and Energy; 5.3.1 Method of Increments; 5.4 Different Approximation Schemes.; 5.4.1 Partitioning and Projection Methods; 5.4.2 Coupled Cluster Method; 5.4.3 Selection of Excitation Operators; 5.4.4 Trial Wavefunctions; 6 Correlated Ground-State Wavefunctions; 6.1 Semiconductors; 6.1.1 Model for Interatomic Correlations; 6.1.2 Estimates of Intra-Atomic Correlations; 6.1.3 Ab Initio Results; 6.2 Ionic and van der Waals Solids. 6.2.1 Three Oxides: MgO, CaO and NiO6.2.2 Rare-Gas Solids; 6.3 Simple Metals; 6.4 Ground States with Strong Correlations: CASSCF; 7 Quasiparticle Excitations; 7.1 Single-particle Green's Function; 7.1.1 Perturbation Expansions; 7.1.2 Temperature Green's Function; 7.2 Quasiparticles in Metals; 7.3 Quasiparticles in Semiconductors and Insulators; 7.3.1 Quasiparticle Approximation; 7.3.2 A Simple Model: Bond-Orbital Approximation; 7.3.3 Wavefunction-Based Ab Inito Calculations; 8 Incoherent Excitations; 8.1 Projection Method; 8.2 An Example: Hubbard Model; 9 Coherent-Potential Approximations. 9.1 Static Disorder9.2 Dynamical Disorder: DMFT and Beyond; 10 Strongly Correlated Electrons; 10.1 Measure of Correlation Strengths; 10.2 Indicators of Strong Correlations; 10.2.1 Low-Energy Scales: a Simple Model; 10.2.2 Effective Hamiltonians; 10.3 Kondo Effect; 10.4 The Hubbard Model Revisited; 10.4.1 Spin-Density Wave Ground State; 10.4.2 Gutzwiller's Ground-State Wavefunction; 10.4.3 Hubbard's Approximations and their Extensions; 10.4.4 Kanamori Limit; 10.5 The t-J Model; 10.6 Mean-Field Approximations; 10.6.1 Test of Different Approximation Schemes; 10.7 Metal-Insulator Transitions. 10.8 Numerical Studies10.9 Break-down of Fermi Liquid Description; 10.9.1 Marginal Fermi Liquid Behavior; 10.9.2 Charged and Neutral Quasiparticles; 10.9.3 Hubbard Chains; 10.9.4 Quantum Critical Point; 11 Transition Metals; 11.1 Ground-State Wavefunction; 11.2 Satellite Structures; 11.3 Temperature-Dependent Magnetism; 11.3.1 Local Spin Fluctuations; 11.3.2 Long-Wavelength Spin Fluctuations; 12 Transition-Metal Oxides; 12.1 Doped Charge-Transfer Systems: the Cuprates; 12.1.1 Quasiparticle-like Excitations; 12.2 Orbital Ordering; 12.2.1 Manganites: LaMnOa and related Compounds.

"It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics."--P. [4] of cover.