UNIVERSITEIT VAN AMSTERDAM Instituut voor Theoretische Fysica

Statistical Physics and Condensed Matter Theory II , second semester 2007/2008

Direct links within this page:

Course description, Literature, Teachers, Schedule, Week-by-week, Assignments and exam.

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Course description

SPCMT II is an optional course in the Master Program Theoretical Physics. At the same time it is open to all interested. We follow up on the introductory course SPCMT I, giving center stage to the Renormalization Group as a conceptual framework and theoretical tool for the analysis of many-body systems and quantum field theories.

Literature

We use the book

`Condensed Matter Field Theory' by Alexander Altland and Ben Simons, Cambridge University Press 2006

A further source are the lecture notes `Kondo problem' (K. Schoutens, UvA 1996)

• Chapter 1-5 of lecture notes Kondo Problem,

• 1994 Les Houches lecture notes by H. Schulz

• 1998 Les Houches lecture notes by S. Girvin.

Teachers

Prof. J. de Boer

Instituut voor Theoretische Fysica
Office 3.57
Tel: 020 - 525 5769/5773

Home page Jan de Boer

Email: jdeboer@...

Prof K. Schoutens

Instituut voor Theoretische Fysica
Office 2.59
Tel: 020 - 525 5664/5773

Home page Kareljan Schoutens

Email: kjs@...

Schedule

Integrated lectures and practice sessions: Wednesday afternoon 1 pm - 4 pm, in room I.101. First session February 6, last session May 21; holidays March 26 and April 30.

Week-by-week

• Week 6, February 6.
  Presentation grand plan; introduction Kondo problem; solution 1D Ising model [AS sect 8.1.1]. Practice: problem 2.4.7.
• Week 7, February 13.
  1D Ising model: scaling and block spin RG [AS sect 8.1]; dissipative quantum tunneling [AS sect 8.2, brief]. Practice: problem 5.5.4.
• Week 8, February 20.
  RG: general theory [AS sect 8.3]. Practice: problem 8.8.5.
• Week 9, February 27.
  Ising: field theory limit and scaling relations [AS sect 8.3.3, 8.4.1]. Final discussion Kondo problem.
• Week 10, March 5.
  RG for phi^4 theory [AS sect 8.4], XY model and KT transition [sect 8.6]. Practice: generalize Ising model field theory limit to the case of a 3-state variable.
• Week 11, March 12.
  XY model and KT transition [sect 8.6.2]. Discussion of solutions to Kondo problem set.
• Week 12, March 19.
  Review of RG and Ginzburg criterion; first introduction of interacting d=1 electrons: RG and bosonization.
• Week 14, April 2.
  RG for interacting electrons in d=1 following Les Houches lecture notes by H. Schulz, section III.A. Exercises: detailed analysis of relevant Feynman diagrams.
• Week 15, April 9.
  Interacting electrons in d=1: bosonization. Exercise: bosonic form of partition sum for particle-hole excitations.
• Week 16, April 16.
  Interacting electrons in d=1: bosonization [AS sect.4.2, 4.3]. Exercise: AS 4.5.4: Boson-fermion duality.
• Week 17, April 23.
  Quantum Hall effect (I): lecture notes Girvin through 1.4. Exercises 1.1 through 1.7.
• Week 19, May 7.
  Quantum Hall effect (II): Girvin 1.5, 1.6 (till page 34)
• Week 20, May 14.
  Back to 1D: quantum wires and quantum Hall edges. Schulz V.A, V.B.
• Week 21, May 21.
  More on CFT and wrap-up.
• Week 22, May 28.
  Question time.
• Week 23, June 4.
  Written exam.

Assignments and exam

Partial credit given for take-home problem sets. The first consists of the 6 problems in the `mid-term' problem set in the 1996 lecture notes on Kondo. The second set has three exercises on RG and bosonization.

• Set I:Kondo problem set
• Set II: RG and bosonization

The final exam will take place Wednesday June 4, 1pm - 4pm, room I.101.

We award up to 18 points for problem set I (P-I) and II (P-II) each. In the final exam (F) up to 90 points are awarded. The grand total will be [10 + max(P-I + P-II + 0.6 F, F)] out of 100.