Chapter 1

An introduction to strongly correlated electron systems. Why there are interesting. The role play by the Mott transition

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2CHAPTER 1. AN INTRODUCTION TO STRONGLY CORRELATED ELECTRON SYSTEMS. WHY THERE ARE INTERESTING. THE ROLE PLAY BY THE MOTT TRANSITION

Renormalization group perspective. Effective hamiltonians

4CHAPTER 2. RENORMALIZATION GROUP PERSPECTIVE. EFFECTIVE HAMILTONIANS

Chapter 3

Effective Action Approach

6 CHAPTER 3. EFFECTIVE ACTION APPROACH

Probes of the solid state. Photoemission Spectra. Other probes of the solid state

8CHAPTER 4. PROBES OF THE SOLID STATE. PHOTOEMISSION SPECTRA. OTHER PROBES OF THE SOLID STATE

Density Functional Theory. Kohn Sham Representation.

10CHAPTER 5. DENSITY FUNCTIONAL THEORY. KOHN SHAM REPRESENTATION.

LMTO’s. ASA and full potential. Application: tight binding

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12CHAPTER 6. LMTO’S. ASA AND FULL POTENTIAL. APPLICATION: TIGHT BINDING

Chapter 7

Hartree Fock

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14 CHAPTER 7. HARTREE FOCK

Chapter 8 LDA+ U

15 16 CHAPTER 8. LDA+ U

Chapter 9

Slave Bosons and Gutzwiller approximation.

18CHAPTER 9. SLAVE BOSONS AND GUTZWILLER APPROXIMATION.

Chapter 10

Mean Field Theory Classical Systems

20 CHAPTER 10. MEAN FIELD THEORY CLASSICAL SYSTEMS

Chapter 11

Mean Field Theory Quantum Systems

22 CHAPTER 11. MEAN FIELD THEORY QUANTUM SYSTEMS

Lattice models and their zero dimensional counterparts.

24CHAPTER 12. LATTICE MODELS AND THEIR ZERO DIMENSIONAL COUNTERPARTS.

Chapter 13

Some simple examples. The falikov Kimball model

26CHAPTER 13. SOME SIMPLE EXAMPLES. THE FALIKOV KIMBALL MODEL

Introduction to the Anderson IMpurity model.

28CHAPTER 14. INTRODUCTION TO THE ANDERSON IMPURITY MODEL.

Chapter 15

Anderson Impurity model. Equations of motion.

30CHAPTER 15. ANDERSON IMPURITY MODEL. EQUATIONS OF MOTION.

Anderson Impurity model. Second Order Perturbation Theory.

32CHAPTER 16. ANDERSON IMPURITY MODEL. SECOND ORDER PERTURBATION THEORY.

Chapter 17

Anderson Impurity model. Exact Diagonalization.

34CHAPTER 17. ANDERSON IMPURITY MODEL. EXACT DIAGONALIZATION.

Chapter 18

Anderson Impurity model. Quantum Montecarlo.

36CHAPTER 18. ANDERSON IMPURITY MODEL. QUANTUM MONTECARLO.

Chapter 19

Anderson Impurity model. Orbitally Degenerate Case

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38CHAPTER 19. ANDERSON IMPURITY MODEL. ORBITALLY DEGENERATE CASE

Mott transition. General arguments for its existence.

40CHAPTER 20. MOTT TRANSITION. GENERAL ARGUMENTS FOR ITS EXISTENCE.

Chapter 21

Mott transition: Hubbard bands.

42 CHAPTER 21. MOTT TRANSITION: HUBBARD BANDS.

Chapter 22

The Friedel -Luttinger Theorem.

44 CHAPTER 22. THE FRIEDEL -LUTTINGER THEOREM.

Results from the Mott transition. Half filled. Transfer of spectral weithg.

46CHAPTER 23. RESULTS FROM THE MOTT TRANSITION. HALF FILLED. TRANSFER OF SPECTRAL WEITHG.

Chapter 24

LDA+ DMFT.

48 CHAPTER 24. LDA+ DMFT.

Chapter 25

Some interesting strongly correlated materials.

50CHAPTER 25. SOME INTERESTING STRONGLY CORRELATED MATERIALS.

Chapter 26

Transition metals Iron and Nickel.

52 CHAPTER 26. TRANSITION METALS IRON AND NICKEL.

Chapter 27 Actinides.

53 54 CHAPTER 27. ACTINIDES.

Chapter 28

LaSrTiO3 3-d doped Mott insulator.

56 CHAPTER 28. LASRTIO3 3-D DOPED MOTT INSULATOR.

Chapter 29

Copper Oxides