M2 ICFP: Statistical Physics for Condensed Matter

Master iCFP - First semester course 2020-2021

Part A: 28 hours divided into seven four hour sessions. Each session has 2 hours of lectures and 2h of tutorials.

Part B is intended for students of the Quantum Physics and Condensed Matter curricula.

Part B: 24 hours divided into six four hour sessions. Each session has 2:30 hours of lectures and 1:30 hours of training exercises. On Monday 02/11, 09/11, 23/11, 30/11, 07/12, 14/12.

Tutorials for part B will take place under the supervision of Tobias Kühn and myself.

Writen xam if possible, on Monday, January 4th, 2021. No documents, no electronic devices (cell, computer or else) allowed. From 08:30 to 12:30 (both E. Trizac's part and mine within the same 4 hour lag, 50% of the final grade each). Else, there will be an oral exam (less than 45', with a topîc to choose from a list some time before the exam itself).

Course outline:

Previously on ICFP Statistical Physics:

PART A by Prof. Emmanuel Trizac

From phase transitions, broken symmetries and universality...

I Introduction to phase transitions and critical phenomena

II First order phase transitions

III Critical phenomena : qualitative approaches

IV Renormalization group ideas

PART B

... Towards condensed matter

I Quantum Phase transitions (3.5 lectures)

1­ Experiments and rationale

2 Ising model in one dimension

3 Quantum rotors

4 Interacting atomic gases

II Disorder, classical and quantum (2.5 lectures)

1­ Classical diffusion in random media

2­ Spin glasses

3­ Localization

4­ Random matrices

Suggested reading for Part I:

[S] p3 thru 8. For the RG analysis of section 3, self-contained accounts can be found in [CL], chapter 5, or in [AS], chapter 8, including the slow mode/fast mode decomposition and the elimination of the latter. For the connections to quantum optics, [PeSm] pp 225-234; [S] pp193-202.

Content of Part I: Define a quantum phase transition and identify the mechanisms playing the role of entropy. Existence of scale invariance and universality classes. Connection to classical thermal phase transitions. Coarse-grained description for continuous phase transitions. Make contact with quantum optics. Technically: the momentum shell RG, Jordan-Wigner in d=1, Bogoliubov transformation for fermions and for bosons.

Suggested reading for Part II:

[H] pp386-397 (on random walks); [N] pp 11-22 (order parameter, replicas, in spin glasses) ; [CC] pp 1-16 (same but somewhat more mathematical).

Content: Quenched vs Annealed disorder. Typical vs rare realizations. Self-averaging. Edwards-Anderson order parameter. Absence of extended states in low dimensions in the presence of disorder.

Technically: Statistics of extremes, the Replica Trick, Replica Symmetry Breaking, Random Matrices.

Material for lecture 10 (23/11/2020) : lecture and tutorial.

Problems

Useful references :

[S] S. Sachdev, Quantum Phase Transitions, Cambridge, 2001.

[PS] L. Pitaevskii and S. Stringari, Bose-Einstein Condensation, Clarendon, Oxford, 2003.

[PeSm] C.J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge, 2008.

[N] H. Nishimori, Statistical physics of spin glasses and information processing: an introduction, Oxford UP, 2001.

[CC] P. Contucci and C. Giardina, Perpsectives on spin glasses, Cambridge UP, 2013.

[H] B. Hugues, Random and Random Environments: vol 2, Random Environments, Oxford UP, 1995.

[Z] R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford, 2001.

[CL] P. Chaikin and T. Lubensky, Principles of condensed-matter physics, Cambridge UP, 1995.

[AS] A. Atland and B. Simons, Condensed-matter field theory, Cambridge UP, 2010.