Introduction / 1: |
Independent Electrons / 2: |
Many-Electron Hamiltonian / 2.1: |
Basis Sets / 2.2: |
Self-consistent Field Equations / 2.3: |
Unrestricted SCF Approximation / 2.4: |
Missing Features of the Independent-Electron Approximation / 2.5: |
Homogeneous Electron Gas / 3: |
Uncorrelated Electrons / 3.1: |
Random-Phase Approximation / 3.2: |
Wigner Crystal / 3.3: |
Density Functional Theory / 4: |
Theory of Hohenberg, Kohn and Sham / 4.1: |
Local-Density Approximation and Extensions / 4.2: |
Strong Electron Correlations: LDA+U / 4.3: |
The Energy Gap Problem / 4.4: |
Time-Dependent DFT / 4.5: |
Wavefunction-Based Methods / 5: |
Method of Configuration Interactions / 5.1: |
Cumulants and their Properties / 5.2: |
Ground-State Wavefunction and Energy / 5.3: |
Method of Increments / 5.3.1: |
Different Approximation Schemes / 5.4: |
Partitioning and Projection Methods / 5.4.1: |
Coupled Cluster Method / 5.4.2: |
Selection of Excitation Operators / 5.4.3: |
Trial Wavefunctions / 5.4.4: |
Correlated Ground-State Wavefunctions / 6: |
Semiconductors / 6.1: |
Model for Interatomic Correlations / 6.1.1: |
Estimates of Intra-Atomic Correlations / 6.1.2: |
Ab Initio Results / 6.1.3: |
Ionic and van der Waals Solids / 6.2: |
Three Oxides: MgO, CaO and NiO / 6.2.1: |
Rare-Gas Solids / 6.2.2: |
Simple Metals / 6.3: |
Ground States with Strong Correlations: CASSCF / 6.4: |
Quasiparticle Excitations / 7: |
Single-particle Green's Function / 7.1: |
Perturbation Expansions / 7.1.1: |
Temperature Green's Function / 7.1.2: |
Quasiparticles in Metals / 7.2: |
Quasiparticles in Semiconductors and Insulators / 7.3: |
Quasiparticle Approximation / 7.3.1: |
A Simple Model: Bond-Orbital Approximation / 7.3.2: |
Wavefunction-Based Ab Inito Calculations / 7.3.3: |
Incoherent Excitations / 8: |
Projection Method / 8.1: |
An Example: Hubbard Model / 8.2: |
Coherent-Potential Approximations / 9: |
Static Disorder / 9.1: |
Dynamical Disorder: DMFT and Beyond / 9.2: |
Strongly Correlated Electrons / 10: |
Measure of Correlation Strengths / 10.1: |
Indicators of Strong Correlations / 10.2: |
Low-Energy Scales: a Simple Model / 10.2.1: |
Effective Hamiltonians / 10.2.2: |
Kondo Effect / 10.3: |
The Hubbard Model Revisited / 10.4: |
Spin-Density Wave Ground State / 10.4.1: |
Gutzwiller's Ground-State Wavefunction / 10.4.2: |
Hubbard's Approximations and their Extensions / 10.4.3: |
Kanamori Limit / 10.4.4: |
The t-J Model / 10.5: |
Mean-Field Approximations / 10.6: |
Test of Different Approximation Schemes / 10.6.1: |
Metal-Insulator Transitions / 10.7: |
Numerical Studies / 10.8: |
Break-down of Fermi Liquid Description / 10.9: |
Marginal Fermi Liquid Behavior / 10.9.1: |
Charged and Neutral Quasiparticles / 10.9.2: |
Hubbard Chains / 10.9.3: |
Quantum Critical Point / 10.9.4: |
Transition Metals / 11: |
Ground-State Wavefunction / 11.1: |
Satellite Structures / 11.2: |
Temperature-Dependent Magnetism / 11.3: |
Local Spin Fluctuations / 11.3.1: |
Long-Wavelength Spin Fluctuations / 11.3.2: |
Transition-Metal Oxides / 12: |
Doped Charge-Transfer Systems: the Cuprates / 12.1: |
Quasiparticle-like Excitations / 12.1.1: |
Orbital Ordering / 12.2: |
Manganites: LaMnO3 and related Compounds / 12.2.1: |
Vanadates: LaVO3 / 12.2.2: |
Ladder Systems: αÆ-NaV2O5 / 12.2.3: |
Other Oxides / 12.2.4: |
Heavy Quasiparticles / 13: |
Kondo Lattice Systems / 13.1: |
Renormalized Band Theory / 13.1.1: |
Large Versus Small Fermi Surface / 13.1.2: |
Mean-Field Treatment / 13.1.3: |
Charge Ordering in Yb4As3: an Instructive Example / 13.2: |
Partial Localization: Dual Role of 5f Electrons / 13.3: |
Heavy d Electrons: LiV2O4 / 13.4: |
Excitations with Fractional Charges / 14: |
Trans-Polyacetylene / 14.1: |
Fractional Quantum Hall Effect / 14.2: |
Correlated Electrons on Frustrated Lattices / 14.3: |
Loop Models / 14.3.1: |
Dimer Models / 14.3.2: |
Mapping to a U(1) Gauge Theory / 14.3.3: |
Magnetic Monopoles / 14.3.4: |
Superconductivity / 15: |
The Superconducting State / 15.1: |
Pair States / 15.1.1: |
BCS Ground State / 15.1.2: |
Cooper Pair Breaking / 15.2: |
Ergodic vs. Nonergodic Perturbations / 15.2.1: |
Pairing Electrons with Population Imbalance / 15.2.2: |
Cooper Pairing without Phonons / 15.3: |
Filled Skutterudite PrOs4Sb12 / 15.3.1: |
UPd2Al3: Pairing and Time-Reversal Symmetry Breaking / 15.3.2: |
Magnetic Resonances / 15.4: |
High-Tc Superconductors / 15.5: |
Suppression of Antiferromagnetic Order by Holes / 15.5.1: |
Pseudogap Regime / 15.5.2: |
Strange Metal / 15.5.3: |
Optical Properties: Drude Peak / 15.5.4: |
Pairing Interactions / 15.5.5: |
Stripe Formation / 15.5.6: |
Some Relations for Cumulants / A: |
Scattering Matrix in Single-Centre and Two-Centre Approximation / B: |
Intra-atomic Correlations in a C Atom / C: |
Landau Parameter: Quasiparticle Mass / D: |
Kondo Lattices: Quasiparticle Interactions / E: |
Lanczos Method / F: |
Density Matrix Renormalization Group / G: |
Monte Carlo Methods / H: |
Sampling Techniques / H.1: |
Ground-State Energy / H.2: |
Computing the Memory Function by Increments / I: |
Kagome Lattice at 1/3 Filling / J: |
References |
Index |
Ladder Systems: α'-NaV2O5 |
Charge Ordering in Yb4As3: an Instructive Example |
Filled Skutterudite PrOs4Sb12 |
Strange-Metal |
1 Sampling Techniques |
2 Ground-State Energy |
Introduction / 1: |
Independent Electrons / 2: |
Many-Electron Hamiltonian / 2.1: |