Many Body 621

 Spring 2023



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 continues from Many Body 620, and will introduce many body physics needed to understand current research activities in quantum condensed matter, including finite temperature methods, response functions,  path integrals, conventional and unconventional superconductivity, strongly correlated electron systems.   I will also review essential material and offer additiional tuition to cater to those who were unable to take 620 last semester.  Please ask Shirley Hinds for a special permission to register. There will be a lot of discussion and interaction. Please register as soon as possible.

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 621
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          Exercise 1
          Exercise 2


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Times: 12.10 Weds and 2 pm Friday in Serin 287. NOTE: We will start on Weds, Jan 18th. Occasionally, to make up for my travel, we will hold an additional  class at a time to be decided.

Office hour:  Time to be decided.  Tel x 9033.

Assessment:   I anticipate four take home exercises. I want to encourage an interactive class and will take this into account when grading.

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  Still to be finalized. This is a very approximate outline that we will adjust after discussion at the first class.

  • Functional Integral Approach to interacting electron systems
  • BCS superconductivity and beyond.  particularly Anisotropic pairing in cuprate sc and superfluid He-3.
  • SYK model
  • Heavy Fermion Materials
  • Twisted Bilayer Graphene

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         Schedule:  UNDER CONSTRUCTION


Extra class
Time: 3pm Mondays

Weds 12.10-1.30 SRN 287

Friday 2.00-3.20pm SRN 287
Jan 16-20

 18 Jan

Introduction to Course.



 20 Jan

  Path integrals and
finite temperature many body physics

  Notes L1

1 Jan 23-27

 25 Jan

Path integrals Bosons

    Notes L2


27 Jan

  Path Integrals:
   Many Bosons

  Notes L3

2 Jan 30-Feb 3

    1st Feb SRN 287

   Sources in Gaussian Ints
   BECs and Superfluids.

   Notes L4

   3rd Feb Serin 287

Spectrum of a superfluid and Critical Velocity

  Notes L5

3 Feb 6-10

   8 Feb SRN 330
  Fermions and Grassman          Numbers: Grassman Calculus

    Notes L6
  10 Feb

   Fermion Path Integral

   Notes L7

4 Feb 13-17

  15 Feb

 Integrating out Fermions

Notes L7

 17 Feb
  Hubbard Stratonovich for Fermions

  Notes L9   
  Notes L10

5 Feb 20-24

  22 Feb

  RPA Approach to the interacting Electron Plasma: electrons in a fluctuating potential field.

Notes L11
  24 Feb

  RPA Approach to the interacting Electron Plasma: Effective Action.

Notes L12

6 Feb 27-Mar 3
2nd March
Make up class

RPA: Screening and Plasmons

Notes L13
3rd March

Bardeen Pines Model

Notes L13
5th March

Fluctuations and
Dissipation I.  Response Functions.

Notes L14

7. Mar 7 -11

8th March

No Class: March Meeting

10th March

No Class: March Meeting

8. Mar 14-18

Spring Break

Spring Break

9. Mar 20-24

22nd March

BCS Theory: Cooper instability.
Pairs as spins.

Notes L19

24th March

Path Integral Formulation of BCS Theory: Effective Action

Notes L20

10.  Mar 27-31

28th March

29th March

Nambu Spinors. Anomalous Greens functions.

Notes L20

31 March

11. Apr 4-8

April 5th
Twisting the phase: Gauge Invariance and Superfluid Stiffness
Notes L20

April 7th BCS Theory
Twisting the Phase: Gauge invariance and Superfluid Stiffness
Notes L20

12. Apr 10-14

April 12th Retardation in BCS Theory;
Migdal Eliashberg
Recording of Class
L20x Notes from Class
April 14th
Eliashberg Equations for phonon-mediated  superconductivity.
Recording of Class
L21 Notes from Class.

13. Apr 18-22

April 19th
Local Moments and Heavy Fermions

14. Apr 25-29

15.  May 2-6

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