Advanced Topics in Condensed Matter

Strongly Correlation and entanglement in Quantum Matter

681 Fall 2019


Piers Coleman   Rutgers University

Images Texts
Times of Course
Syllabus outline


  Phase diagram of Magic Angle


Magic Angle Graphene

Illustrating the Effective Action in Path Integral


Relationship between Meissner Effect and Phase Rigidity of a Superconductor.

Gap Structure of a d-wave superconductor
115 Superconductor

Phase Diagram of the Kondo Effect

CeCoIn5: a 115 Superconductor

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Instructor: Piers Coleman, Room 268
If you have any questions about this course or the homework, please do not hesitate to contact me via email at : coleman@physics.rutgers.edu

Scope of Course. This course will provide a selected introduction to strongly correlated electron systems.   There will be a lot of discussion and interaction. The course will begin with a  discussion  of broken symmetry and superconductivity.  We will then shift to a new topic: Magic Angle Graphene, discussing the recent developments in this field and the Bistritzer-Macdonald picture of these materials.  We will end with a  local moment formation, the Kondo Lattice and the physics of heavy fermion materials and quantum criticality.  The course will be based in part on the last seven chapters of my book, "Introduction to Many-Body Physics" and on a recent series of lectures at the 2019 ICAM Cargese School on emergent physics of quantum materials.

Students with disabilities 

Introduction to Many-Body Physics

The  reference texts will be
    ``Introduction to Many-Body Physics'', Piers Coleman, (CUP, Jan 2016). Chapters 12-18.

      Here are some additional useful references:

      • Condensed Matter Field Theory by Alexander Altland and Ben Simons.(CUP, 2006)
        An excellent introduction to Field Theory applied in condensed matter physics. 
      • Advanced Solid State Physics by Philip Phillips, second edition (CUP, 2012).
      • Basic Notions in Condensed Matter Physics by P. W. Anderson, Benjamin Cummings 1984. 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.
      • Quantum Field Theory in Condensed Matter Phyiscs,  A. M. Tsvelik, Cambridge University Press, 2nd edition (2003).
      • 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.

      Traditional Many Body Theory and Greens Functions

      • ``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. Reprinted by Dover.
      • ``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 exercises! However, it is the only one of this set to touch on the subject of functional integrals.

      Further references:

      • The Theory of Quantum Liquids by D. Pines and P. Nozieres. Excellent introduction to Fermi liquid theory that avoids the use of field theory.
      • Statistical Physics, vol II by Lifshitz and Pitaevskii. Pergammon. Marvellous book on applications of many body physics, mainly to condensed matter physics.

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

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Exercises 681
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    Exercise 1


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Times: 3.20 pm on Monday  and 3.20 pm on Monday in  ARC 108. We will start on Weds Sep 5. Occasionally, to make up for my travel, we will hold an additional  class,  on Friday 12.30-1.40pm, SEC 206.

Office hour:  Officially:  9.50am Fridays  but come by if you have questions.  Tel x 9033.

Assessment:   I anticipate four or five take home exercises and one take-home final. I want to encourage an interactive class and will take this into account when grading!

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  Here is the provisional outline.

  • Functional Integral Approach to interacting electron systems
  • Superconductivity,  particularly Anisotropic pairing and superfluid He-3.

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Mon 3.20-4.40 ARC 108

Weds 3.20-4.40 Arc 108

Extra class
Time: 12.00-1.20pm
Place: SEC 206

1.Sep 2-6

5th Sept 1.40 ARC 108
First Class of Semester

Introduction and early history

2 Sep 9-13
London's arguments
Coherent states
Ginzburg Landau Theory.
Flux Quanta and Type II Superconductors
Extra Class?

3 Sep 16-20
BCS Tool Box I
BCS Tool Box II

4 Sep 23-27

 No Class No Class

5 Sept 30-Oct 4
Retardation and anisotropic pairing: BCS theory with momentum dependent coupling.  Anisotropic pairing:
superfluid He-3A and B

6 Oct 7-11

7. Oct 14-18
Starting Magic Angle Graphene around now

8. Oct 21-25

9. Oct 28-Nov 1

10.  Nov 4-8

No Class

11.  Nov 11-15

12.  Nov 18-22

No Class

13.  Nov 25-29

No Class Thanksgiving

14.  Dec 2-6

15.  Dec 9-13

Last Day of Classes


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