Advanced Topics in Condensed Matter

Strongly Correlated Electrons: electrons at the Brink of Magnetism.

682A Spring 2015

Piers Coleman, Rutgers University

Images Texts
Times of Course
Syllabus outline



Discrete construction of a path integral

Illustrating the Effective Action in Path Integral

Relationship between Meissner Effect and Phase Rigidity of a Superconductor.

Gap Structure of a d-wave superconductor

Phase Diagram of the Kondo Effect

Topological (Kondo )Insulators.

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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 an introduction to strongly correlated electron systems.   Starting with a path-integral approach to many body physics, we will revisit  superconductivity, going on to discuss itinerant magnetism, anisotropic superconductivity,  local moment formation, the Kondo Lattice and the physics of heavy fermion materials: metals, superconductors, topological Kondo insulators and if we have time, quantum criticality.  The course will be based on the last seven chapters of my book, "Introduction to Many-Body Physics".

Students with disabilities 

Introduction to Many-Body Physics

The  reference texts will be
    ``Introduction to Many-Body Physics'', Piers Coleman, (CUP, Dec 2015). Chapters 12-18.
    (To be provided as course material.)

``Heavy Fermions: Electrons at the Brink of Magnetism"

(Handbook of Magnetism and Advanced Magnetic Materials. Edited by Helmut Kronmuller and Stuart Parkin. Vol 1: Fundamentals and Theory. John Wiley and Sons, 95-148 (2007).)

      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 628
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         Homework 1    Solution 1
         Homework 2    Solution 2
         Homework 3
         Final Take Home

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Times: 1.40 pm on Monday  and 1.40 pm on Monday in  Serin-401. We will start on Weds Jan 21. Occasionally, to make up for my travel, we will hold an additional  class, on Thursdays 1.40-3pm Serin 287 (Condensed Matter Reading room). 

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.
  • Local Moment Formation
  • Heavy Fermions and the Kondo Lattice.
  • Mixed Valence and Topological Kondo Insulators

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Mon 1:40-3:00 Serin 401

Weds 1:40 Serin 401

Extra class
Time: Thursday

CMT Reading Room

1.Jan 19-23

21st Jan. 1.40 Serin 401
First Class of Semester
Why path integrals?
Coherent states and the bosonic path integral.

2 Jan 26-30
Fermions with path integrals.
The Hubbard Stratonovich transformation, the concept of the effective action and the link with Landau Theory.
Jan 29th. 1.40 Serin 287
Some simple Examples.

3 Feb 2-6
Itinerant Magnetism from path integrals: the Ferromagnet. Zero point magnetic fluctuations and and quantum critical points.

4 Feb 9-13

No Class

No Class

5 Feb16-20
BCS Theory with path integrals.
Nambu Green's function and tunneling density of states.
Feb 19th Superfluid stiffness as phase rigidity.

6 Feb 23-27
Retardation and anisotropic pairing: BCS theory with momentum dependent coupling.
Retardation and the Coulomb pseudopotential.
Anisotropic superconductivity: d-wave pairing.

7. Mar 2-6
Anisotropic pairing: superfluid He-3.  Nambu matrices for spin.
Anisotropic pairing:
superfluid He-3B and the Balian Werthammer State.
Calculation of Knight Shift.

8. Mar 9-13

9. Mar 16-20

Spring Break

Spring Break

Spring Break

10.  Mar 23-27

No Class
March 26th Extra

11.  Mar 30-April 3

12.  Apr 6-10

April 9th Extra

13.  Apr 13-17

No Class

No Class

14.  Apr 20-24

15.  Apr 27-May 1

16.  May 4
Last class

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