8/23/18

Advanced Topics in Condensed Matter

Strongly Correlation and entanglement in Quantum Matter

681 Fall 2018

Update: We are going to combine physics 681 and physics 603, which will now be taught by
Piers Coleman (5 Sept - Oct 24) and Kristjan Haule (Oct 29-Dec 12)      

Piers Coleman and Kristjan Haule,  Rutgers University

Images Texts
Exercises
Times of Course
Syllabus outline
Timetable

 


   

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.

(Return to top)


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.   There will be a lot of discussion and interaction. Starting with a path-integral approach to many body physics, we will discuss broken symmetry in magnetism and superconductivity, going on to discussanisotropic superconductivity,  local moment formation, the Kondo Lattice and the physics of heavy fermion materials and quantum criticality.  We will end with a discussion of topological matter, including the quantum Hall effect and the strong topological insulator.   The course will be based in part 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, 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).

(Return to top)



Exercises 681
(Return to top)

      

(Return to top)       


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,  at a time to be determined. Bring your schedules to the first class!

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!

(Return to top)



Outline
  Here is the provisional outline.

  • Functional Integral Approach to interacting electron systems
  • Superconductivity,  particularly Anisotropic pairing and superfluid He-3.
  • Heavy Fermions and the Kondo Lattice.
  • Topological Matter: from the Quantum Hall Insulator to Topological Kondo Insulators



(Return to top)

         Schedule:


Week


Mon 3.20-4.40 ARC 108


Weds 3.20-4.40 Arc 108

Extra class
Time: Time and Place to be determined.



1.Sep 3-7


5th Sept 1.40 ARC 108
First Class of Semester

Landau Theory.




2 Sep 10-14
Why path integrals?
Coherent states and the bosonic path integral.
Fermions with path integrals.

3 Sep 17-21
Fermions with path integrals. The Hubbard Stratonovich transformation, the concept of the effective action and the link with Landau Theory.

4 Sep 24-28

 Itinerant Magnetism from path integrals: the Ferromagnet. BCS Theory with path integrals.




5 Oct 1-5
Nambu Green's function and tunneling density of states.  Superfluid stiffness as phase rigidity;

6 Oct 8-12
No Class Oct 8
Superfluid stiffness as phase rigidity. Retardation and anisotropic pairing: BCS theory with momentum dependent coupling.

7. Oct 15-19
Retardation and the Coulomb pseudopotential.
Anisotropic superconductivity: d-wave pairing.
Anisotropic pairing: superfluid He-3B.  Nambu matrices for spin.

8. Oct 22-26
Anisotropic pairing:
superfluid He-3A and B



9. Oct 29-Nov 2
No Class







10.  Nov 5-9

No Class



11.  Nov 12-16




12.  Nov 19-23

No Class (Thanksgiving)



13.  Nov 26-30






14.  Dec 3-7




15.  Dec 10-14

Last Day of Classes

 






(Return to top)