Physics of strongly correlated systems

Fall 2005

Donglai Feng, Fudan University

  Download Texts
 Exercises
 Evaluation scheme
 Syllabus outline
 Timetable
 



Instructor: 封东来

If you have any enquiries about this course or the homework, please do not hesitate to contact me via email at : dlfeng@fudan.edu.cn

Office hour:   By arrangement.  Tele: 23486, 先进材料楼 412

TA: 沈大伟

Email: dwshen@fudan.edu.cn       Tele: 55664482          先进材料楼 210

Scope of Course. The physics of strongly correlated systems is one of the main theme in condensed matter physics. This course introduces you to the main techniques, concepts and phenomena in this field.

When & Where: 8:55am on every Thursday starting September 8th in 逸夫科技楼四楼会议室
If I had to travel and cancel certain class, we will arrange an alternate class at 7:00PM in room 202 of the advanced material building later on.
 



    Download the course materials (ftp://srp:srp@10.46.1.199, only for internal use within Fudan) and study them before the class.

  • Lecture 1:
  1. unfinished frontier -- P. Coleman's view of the history (mainly theory side)
  2. 冯端 seminar at Fudan
  3. 冯端，金国钧《凝聚态物理学（上卷）》纵览
  • Lecture 2,3:
  1. Fazekas, "Lecture notes on Electron Correlation and Magnetism" Chaps.2,3
  2. 冯端，金国钧《凝聚态物理学（上卷）》Chap. 11
  • Lecture 4:
  1. three videos on Fermi liquid and photoemission spectroscopy
  2. Schultz's paper on Fermi liquid


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Texts:

  • Patrik Fazekas, "Lecture notes on Electron Correlation and Magnetism"
  • 冯端，金国钧《凝聚态物理学（上卷）》 -- an excellent introductory book on wide area of condensed matter physics, available in the bookstore
  • P. M. Chaikin "Principles of condensed matter physics"  -- a nice pedagogical book on ideas of phase transition, correlation functions, 世图版available in bookstore
     

References

  • N. Tsuda et al. "Electonic conduction in oxides"
  • P. A. Cox "Introduction to transition metal oxides"
  • M. Imada "Metal-insulator transitions" @ Review of Modern Physics, Vol 70, 1039 (1998)
  • Carl J. Ballhausen "Introduction to Ligand Field Theory"
  • N. F. Mott "Metal-Insulator transition"
  • The Theory of Quantum Liquids by D. Pines and P. Nozieres. Excellent introduction to Fermi liquid theory that avoids the use of field theory.

     

More theoretical references



     Overview
    • Basic Notions in Condensed Matter Physics by P. W. Anderson. A classic reference. Many of us still turn to this book for inspiration, and philosophy. It also has a fine selection of important reprints at the back.


    Traditional Many Body Theory and Greens Functions
     

    • ``Many-Particle Physics'', Third Edition  by G. Mahan. (Plenum).
    • ``Methods of Quantum Field Theory in Statistical Physics'' by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD.
    • ``A guide to Feynman Diagrams in the Many-Body problem by R. D. Mattuck. A light introduction to the subject.
    • ``Greens functions for Solid State Physics'' S.Doniach and E. H. Sondheimer. Not as thorough as AGD, but less threatening and somehow more manageable. Frontiers in Physics series no 44.
    • ``Quantum Many Particle Systems'' by J. W. Negele and H. Orland. Alas all the good physics is in the unsolved excercises! However, it is the only one of this set to touch on the subject of functional integrals.


    Newer approaches to Many-Body Problem.
     

    • R. Shankar, Rev Mod Phys 66 129 (1994). An amazingly self-contained review of the renormalization group and functional integral techniques written by one of the best expositors of condensed matter physics.
    • ``Field Theories of Condensed Matter Physics'' by E. Fradkin. (Frontiers in Physics, Addison Wesley). Interesting material on the fractional statistics and the fractional quantum Hall effect.
    • ``Quantum Field Theory in Condensed Matter Physics'' by A. Tsvelik. (Cambridge paper back) Very good for one dimensional systems. No excercises.


    Further references:

    • Statistical Physics, vol II by Lifshitz and Pitaevskii. Pergammon. Marvellous book on applications of many body physics, mainly to condensed matter physics.

    Online references     (Check it out- this is a great link).

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Exercises 

          Exercise 1    (pdf) ,   Solutions to Exercise 1 (pdf)
          Exercise 2    (pdf) ,   Solutions to Exercise 2 (pdf)
          Exercise 3    (pdf) ,   Solutions to Exercise 3 (pdf)
          Exercise 4    (pdf) ,   Solutions to Exercise 4 (pdf)
          Exercise 5    (pdf) ,   Solutions to Exercise 5 (pdf)

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Evaluation scheme 

five homeworks 4%*5=20%
one in-class, close-book, midterm exam 20%
final presentations 30%
email good questions on class material before class (2 points each max.5) 10%
answer questions and raise questions in class (3 points each, max. 7) 20%
 

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Outline  

  • Introduction to Multi-electron atom and molecule, Ligand field theory and Molecular orbital theory
  • Fermi liquid theory
  • Hubbard model and its extensions, Mott metal-insulator transition and spin-charge separation
  • Anderson impurity model and Kondo effect
  • Screening, electron-phonon interaction, BCS theory
  • Phase transition, order parameter, and quantum criticality
  • High Tc superconductivity
  • Orbital ordering, manganite
  • Spectroscopy techniques in many body physics.



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Week Thursday


Plan
1 Sept 8
 Introduction
2 Sept 15
 Theories for atoms, molecules, and ligand field theory for solids
3 Sept 22
 Exchange interactions
4 Sept 29
 Fermi Liquid Theory, Green's Functions
5 Oct 6

No class
6 Oct 13
7 Oct 20
8 Oct 27
9 Nov 3
10 Nov 10
 Mid term close book exam
11 Nov 17
12 Nov 24
13 Dec 1
  
14 Dec 8
15 Dec 15
16 Dec 22
  
17 Dec 29  
18 Jan 5 Final presentation 1
19 Jan 12 Final presentation 2

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