Phy250 (Fall 2013)

 "Demystifying" Quantum Field Theory

 
Classes: Lectures Tu-Thu 2:00-3:30pm, Leconte 385. Discussion Session (by announcement).
Office Hours: (to appear).
 
 
Outline:
This is a special topics course aimed at graduate students interested either in modern condensed matter theory or high energy physics. The central
theme of this course will be to demonstrate how field theory is often the natural tool to describe a wide range of quantum systems, and the bag of
tricks that can be employed to study them.

We will discuss a number of different lattice models and show how the long distance physics is naturally described in terms of a field theory.
Techniques such as low and high temperature expansion, large-N techniques, as well as the renormalization group, dualities and exact solutions will be discussed.
These will be applied to models of spontaneous symmetry breaking describing superfluidity and magnetism.
 
We will also discuss exotic phases with topological order, such as fractional quantum Hall states and spin liquids and how they can be naturally described by gauge theories.

Suggested Books:
1. Gauge Fields and Strings: A. Polyakov
2. Quantum Field Theory of Many Body Systems: X. G. Wen
3. Quantum Phase Transitions. Subir Sachdev.

Evaluation 35% Assignments, 10% Class participation, 55% Final Project  [for 2 credits, no final project]

Problem Set 1:[Due Oct 31]
Solutions: Problems 1,2 [Sol. Part 1]
                   Remaining problems [Sol. Part 2]

Problem Set 2: [Due Dec 9]
Solutions: [Soln PS2]
Pick up graded problem sets from Itamar Kimchi in Birge 521 on Wednesday, Dec 18


Lecture Notes (FALL 2013)



  • Sep 19, 24: Spontaneous breaking of continuous Symmetry

  • Sep 26, Oct 1: Superfluid - Superconductor Duality and Transition:
    • Anderson Tower: NOTES
    • Duality in 2+1D: NOTES
    • Transition in the large N limit: NOTES
  • Oct 3, 8, 10: Superfluids and Insulators in 1+1 Dimension
    • Duality and Phases of 1+1 D Bose Hubbard model. NOTES
    • 1+1 D Bose Hubbard Model at Half Filling. Role of Berry Phases.

  • Oct 15-29: Gauge Theories in Condensed Matter Physics:
    • Z2 gauge theories. Confinement and Deconfinement. NOTES
    • Topological order. NOTES
    • Anyon statisitics in the Toric Code. Kitaev-Laumann Note on Arxiv
    • topological entanglement entropy Notes
    • U(1) gauge theories and Polyakov Mechanism [Origin in Solid State Physics - Notes]




Topics and Class Schedule from a previous offering of this course (Spring 2012)

 Jan 31  - Feb 2
 Transverse Field Ising Model in D=1 and Field theory description. Lec Feb 2 Lec Jan 31; Powerpoint Jan 31
 Feb 7 -    Feb 9
 Quantum-Classical Mapping (Feb 7 Lecture). Ref: Polyakov, pg 10; Sachdev pg. 13-20. Duality of D=2 Ising Model. (Feb 9 Lecture) Ref: Wen pg 250, Kogut RMP pg. 681-689.
 Feb 14    Feb 16
 Ising Gauge Theory and Topological Order. Ref. Wen pg 250. Review by Senthil. (Fractionalization and Gauge theories). Review by Balents (Spin liquids and Gauge theories)
 Feb 21    Feb 23
U(1) Gauge theories and Quantum Spin systems Notes. The Polyakov Mechanism. (Ref: Coherent state path integral, by Fradkin)
 Feb 28    Mar 1
 March Meeting (No class Tuesday).  THURSDAY: U(1) Gauge theories and quantum spin systems [Ref: Auerbach (see Bspace).]
 Mar 6     Mar 8
  U(1) Gauge theories and quantum spin systems  [Review Article, pg28-38]. Superfluidity and Bose Hubbard Model.
 Mar 13  Mar 15
 Superflidity - conceptual issues (Anderson Review). Mean Field Phase Diagram [see Bspace and Fisher et al. PRB 40, pg 546-550]. NOTES
 Mar 20  Mar 22
 Anderson tower (NOTES) , Duality to superconductor (NOTES). Mott-Superfluid transition in Large-N limit. (NOTES)
 Mar 27  Mar 29
 Spring Break
 Apr 3    Apr 5
 Mott-Superfluid transition in D=1+1 and Berry Phase. (NOTES)
 Apr 10  Apr 12
 Fractional Quantum Hall Effect [Girvin Review, ArovasSchriefferWilczek]
 Apr 17  Apr 19
 Composite Bosons and Fermions [Zhang, Kivelson, Hansson] [Jain]
 Apr 24  Apr 26

Chern Simons Theory [Wen Book]


 
Subpages (1): Project Topics
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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PS1.pdf
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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Ashvin Vishwanath,
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