'This book serves the purpose of introducing the reader to the variety of advanced techniques available to study electron correlations in condensed systems.' d Science

• 1. Outline.- 2. Electron Density, Density Matrices and Atomic Properties.- 3. Homogeneous and Inhomogeneous Electron Assemblies.- 4. Localized versus Molecular Orbital Theories of Electrons.- 5. Quantum Monte Carlo Calculation of Correlation Energy.- 6. Quasiparticles and Collective Excitations (Especially Plasmons).- 7. Metal-Insulator Transitions and the Chemical Bond.- 8. Electronic Correlation in Disordered Systems (Especially Liquid Metals).- 9. Magnetically Induced Wigner Solid.- Appendixes.- Appendix to Chapter 2.- A2.1. Density Matrices for Many-Particle Oscillator Model.- A2.2. Atomic Energies from Renormalization of Large-Dimensionality Results.- A2.3. Size-Extensivity, Cumulants, and Coupled-Cluster Equations.- A2.3.1. Different Representations of ?.- A2.3.2. Calculating the Ground-State Energy.- A2.3.3. Derivation of the Coupled-Cluster Equations.- A2.3.4. Independent Mode Approximation.- A2.4. The Hiller—Sucher—Feinberg Identity and Improvement of Cusp Condition.- A2.5. Two Electrons with Coulomb Interaction Moving in an External Oscillator Potential.- A2.5.1. Solution of Schrödinger Equation.- A2.5.2. An Exact Solution.- A2.5.3. Results.- A2.5.4. Some Physical Consequences.- Appendix to Chapter 3.- A3.1. Example of Spin Density Description: Bloch’s Hartree—Fock Treatment.- A3.2. Wave-Number Dependent Magnetic Susceptibility.- A3.3. Koster—Slater-Like Model of Criterion for Local Moment Formation.- A3.4. Dynamic Properties of Jellium.- A3.4.1. Response Function and Screening.- A3.4.2. Random Phase Approximation and Beyond.- A3.5. Static Local-Field and Dielectric Function Applied to Screened Interactions in Metals.- Appendix to Chapter 4.- A4.1. Model of Two-Electron Homopolar Molecule.- A4.2. Dependence on Atomic Number of Correlation Energiesin Neutral Atoms.- A4.3. Correlation Energy of Diatomic Molecules versus Number of Electrons.- A4.4. Effect of Correlation on von Weizsäcker Inhomogeneity Kinetic Energy: Scaling Properties and Molecular Dissociation.- Appendix to Chapter 5.- Appendix to Chapter 6.- A6.2. Thomas—Fermi Model of Static Dielectric Function of Semiconductor.- A6.3. Semiempirical Self-Energy Corrections to Density Functional (LDA) Bands of Semiconductors.- A6.3.1. Summary of Technique.- A6.3.2. Some Specific Examples.- A6.5. Coefficients in the Continued Fraction Expansion.- A6.6. Plasmon Properties and Effective Screened Interaction.- A6.6.1. Screened Interaction.- A6.6.2. Plasmon Properties.- A6.7 Some Difficulties with Plasmon-Pole Approximations and Proposed Remedies.- A6.8 Different Forms of GW Approximations.- A6.8.1. Vertices and Self-Energies.- A6.8.2. Summary of Effects of Exchange and Correlation.- Appendix to Chapter 7.- A7.1. Relation of Resonating Valence Bond and Gutzwiller Methods.- A7.2. Reduction of Hubbard and Emery Models to Effective Spin Hamiltonians.- A7.2.1. Hubbard Hamiltonian with Strong Electron Repulsion Energy.- A7.2.2. Emery Model.- A7.3. Luttinger Liquid: Spinons and Holons.- A7.3.1. Spin—Charge Separation.- A7.3.2. Can a 2D Luttinger Liquid Exist?.- A7.3.3. Spinons, Holons and Gapless Spin Excitations.- A7.5. Electron Liquids Flowing through Antiferromagnetic Assemblies.- Appendix to Chapter 9.- A9.1. Electron Liquids and the Quantized Hall State.- A9.2. Melting Criteria for Three-Dimensional Classical and Quantal Wigner Crystals.- A9.3. Wigner Oscillator in Magnetic Field of Arbitrary Strength.- A9.4. Shear Modulus, Electron Density Profile, and Phase Diagram for Two-Dimensional Wigner Crystals.- A9.4.1. Observation of Magnetically Induced Wigner Solid(MIWS).- A9.4.2. Electron Density Profile and Shear Modulus.- A9.4.3. Limiting Cases: Instabilities and Melting.- A9.4.4. The Magnetically Induced Wigner Solid (MIWS).- A9.4.5. Discussion and Summary.- References.

'This book serves the purpose of introducing the reader to the variety of advanced techniques available to study electron correlations in condensed systems.' d Science

• 1. Outline.- 2. Electron Density, Density Matrices and Atomic Properties.- 3. Homogeneous and Inhomogeneous Electron Assemblies.- 4. Localized versus Molecular Orbital Theories of Electrons.- 5. Quantum Monte Carlo Calculation of Correlation Energy.- 6. Quasiparticles and Collective Excitations (Especially Plasmons).- 7. Metal-Insulator Transitions and the Chemical Bond.- 8. Electronic Correlation in Disordered Systems (Especially Liquid Metals).- 9. Magnetically Induced Wigner Solid.- Appendixes.- Appendix to Chapter 2.- A2.1. Density Matrices for Many-Particle Oscillator Model.- A2.2. Atomic Energies from Renormalization of Large-Dimensionality Results.- A2.3. Size-Extensivity, Cumulants, and Coupled-Cluster Equations.- A2.3.1. Different Representations of ?.- A2.3.2. Calculating the Ground-State Energy.- A2.3.3. Derivation of the Coupled-Cluster Equations.- A2.3.4. Independent Mode Approximation.- A2.4. The Hiller—Sucher—Feinberg Identity and Improvement of Cusp Condition.- A2.5. Two Electrons with Coulomb Interaction Moving in an External Oscillator Potential.- A2.5.1. Solution of Schrödinger Equation.- A2.5.2. An Exact Solution.- A2.5.3. Results.- A2.5.4. Some Physical Consequences.- Appendix to Chapter 3.- A3.1. Example of Spin Density Description: Bloch’s Hartree—Fock Treatment.- A3.2. Wave-Number Dependent Magnetic Susceptibility.- A3.3. Koster—Slater-Like Model of Criterion for Local Moment Formation.- A3.4. Dynamic Properties of Jellium.- A3.4.1. Response Function and Screening.- A3.4.2. Random Phase Approximation and Beyond.- A3.5. Static Local-Field and Dielectric Function Applied to Screened Interactions in Metals.- Appendix to Chapter 4.- A4.1. Model of Two-Electron Homopolar Molecule.- A4.2. Dependence on Atomic Number of Correlation Energiesin Neutral Atoms.- A4.3. Correlation Energy of Diatomic Molecules versus Number of Electrons.- A4.4. Effect of Correlation on von Weizsäcker Inhomogeneity Kinetic Energy: Scaling Properties and Molecular Dissociation.- Appendix to Chapter 5.- Appendix to Chapter 6.- A6.2. Thomas—Fermi Model of Static Dielectric Function of Semiconductor.- A6.3. Semiempirical Self-Energy Corrections to Density Functional (LDA) Bands of Semiconductors.- A6.3.1. Summary of Technique.- A6.3.2. Some Specific Examples.- A6.5. Coefficients in the Continued Fraction Expansion.- A6.6. Plasmon Properties and Effective Screened Interaction.- A6.6.1. Screened Interaction.- A6.6.2. Plasmon Properties.- A6.7 Some Difficulties with Plasmon-Pole Approximations and Proposed Remedies.- A6.8 Different Forms of GW Approximations.- A6.8.1. Vertices and Self-Energies.- A6.8.2. Summary of Effects of Exchange and Correlation.- Appendix to Chapter 7.- A7.1. Relation of Resonating Valence Bond and Gutzwiller Methods.- A7.2. Reduction of Hubbard and Emery Models to Effective Spin Hamiltonians.- A7.2.1. Hubbard Hamiltonian with Strong Electron Repulsion Energy.- A7.2.2. Emery Model.- A7.3. Luttinger Liquid: Spinons and Holons.- A7.3.1. Spin—Charge Separation.- A7.3.2. Can a 2D Luttinger Liquid Exist?.- A7.3.3. Spinons, Holons and Gapless Spin Excitations.- A7.5. Electron Liquids Flowing through Antiferromagnetic Assemblies.- Appendix to Chapter 9.- A9.1. Electron Liquids and the Quantized Hall State.- A9.2. Melting Criteria for Three-Dimensional Classical and Quantal Wigner Crystals.- A9.3. Wigner Oscillator in Magnetic Field of Arbitrary Strength.- A9.4. Shear Modulus, Electron Density Profile, and Phase Diagram for Two-Dimensional Wigner Crystals.- A9.4.1. Observation of Magnetically Induced Wigner Solid(MIWS).- A9.4.2. Electron Density Profile and Shear Modulus.- A9.4.3. Limiting Cases: Instabilities and Melting.- A9.4.4. The Magnetically Induced Wigner Solid (MIWS).- A9.4.5. Discussion and Summary.- References.

'This book serves the purpose of introducing the reader to the variety of advanced techniques available to study electron correlations in condensed systems.' d Science

• 1. Outline.- 2. Electron Density, Density Matrices and Atomic Properties.- 3. Homogeneous and Inhomogeneous Electron Assemblies.- 4. Localized versus Molecular Orbital Theories of Electrons.- 5. Quantum Monte Carlo Calculation of Correlation Energy.- 6. Quasiparticles and Collective Excitations (Especially Plasmons).- 7. Metal-Insulator Transitions and the Chemical Bond.- 8. Electronic Correlation in Disordered Systems (Especially Liquid Metals).- 9. Magnetically Induced Wigner Solid.- Appendixes.- Appendix to Chapter 2.- A2.1. Density Matrices for Many-Particle Oscillator Model.- A2.2. Atomic Energies from Renormalization of Large-Dimensionality Results.- A2.3. Size-Extensivity, Cumulants, and Coupled-Cluster Equations.- A2.3.1. Different Representations of ?.- A2.3.2. Calculating the Ground-State Energy.- A2.3.3. Derivation of the Coupled-Cluster Equations.- A2.3.4. Independent Mode Approximation.- A2.4. The Hiller—Sucher—Feinberg Identity and Improvement of Cusp Condition.- A2.5. Two Electrons with Coulomb Interaction Moving in an External Oscillator Potential.- A2.5.1. Solution of Schrödinger Equation.- A2.5.2. An Exact Solution.- A2.5.3. Results.- A2.5.4. Some Physical Consequences.- Appendix to Chapter 3.- A3.1. Example of Spin Density Description: Bloch’s Hartree—Fock Treatment.- A3.2. Wave-Number Dependent Magnetic Susceptibility.- A3.3. Koster—Slater-Like Model of Criterion for Local Moment Formation.- A3.4. Dynamic Properties of Jellium.- A3.4.1. Response Function and Screening.- A3.4.2. Random Phase Approximation and Beyond.- A3.5. Static Local-Field and Dielectric Function Applied to Screened Interactions in Metals.- Appendix to Chapter 4.- A4.1. Model of Two-Electron Homopolar Molecule.- A4.2. Dependence on Atomic Number of Correlation Energiesin Neutral Atoms.- A4.3. Correlation Energy of Diatomic Molecules versus Number of Electrons.- A4.4. Effect of Correlation on von Weizsäcker Inhomogeneity Kinetic Energy: Scaling Properties and Molecular Dissociation.- Appendix to Chapter 5.- Appendix to Chapter 6.- A6.2. Thomas—Fermi Model of Static Dielectric Function of Semiconductor.- A6.3. Semiempirical Self-Energy Corrections to Density Functional (LDA) Bands of Semiconductors.- A6.3.1. Summary of Technique.- A6.3.2. Some Specific Examples.- A6.5. Coefficients in the Continued Fraction Expansion.- A6.6. Plasmon Properties and Effective Screened Interaction.- A6.6.1. Screened Interaction.- A6.6.2. Plasmon Properties.- A6.7 Some Difficulties with Plasmon-Pole Approximations and Proposed Remedies.- A6.8 Different Forms of GW Approximations.- A6.8.1. Vertices and Self-Energies.- A6.8.2. Summary of Effects of Exchange and Correlation.- Appendix to Chapter 7.- A7.1. Relation of Resonating Valence Bond and Gutzwiller Methods.- A7.2. Reduction of Hubbard and Emery Models to Effective Spin Hamiltonians.- A7.2.1. Hubbard Hamiltonian with Strong Electron Repulsion Energy.- A7.2.2. Emery Model.- A7.3. Luttinger Liquid: Spinons and Holons.- A7.3.1. Spin—Charge Separation.- A7.3.2. Can a 2D Luttinger Liquid Exist?.- A7.3.3. Spinons, Holons and Gapless Spin Excitations.- A7.5. Electron Liquids Flowing through Antiferromagnetic Assemblies.- Appendix to Chapter 9.- A9.1. Electron Liquids and the Quantized Hall State.- A9.2. Melting Criteria for Three-Dimensional Classical and Quantal Wigner Crystals.- A9.3. Wigner Oscillator in Magnetic Field of Arbitrary Strength.- A9.4. Shear Modulus, Electron Density Profile, and Phase Diagram for Two-Dimensional Wigner Crystals.- A9.4.1. Observation of Magnetically Induced Wigner Solid(MIWS).- A9.4.2. Electron Density Profile and Shear Modulus.- A9.4.3. Limiting Cases: Instabilities and Melting.- A9.4.4. The Magnetically Induced Wigner Solid (MIWS).- A9.4.5. Discussion and Summary.- References.