"Demystifying" Quantum Field Theory[NEW] Project Topics: Classes: Lectures Tu-Thu 2:00-3:30pm, Evans 9. Discussion Session (by announcement): Wed 5-6pm, 385 Leconte.Office Hours: Thursday 4-5pm.Presentations: 325 Leconte Tuesday May 4, 3:00-5:00pm AND Thursday May 6, 2:00-3:30pm. [Schedule]Course GSI: Pavan HosurOutline:This is a special topics course aimed at graduate students interested in modern condensed matter theory and also 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. Polyakov2. Quantum Field Theory of Many Body Systems: X. G. Wen Evaluation 35% Assignments, 15% Class participation, 50% Project [for 2 credits, no project]Problem Sets:Problem Set 1 : Due March 9. Problem Set 2 :
[Final Version] Due May 7Lecture Notes:Lectures 2 and 3 (Jan 21&26): Transverse Field Ising Model I (Weak and strong coupling, Duality)
Discussion Session (Jan 27): Second Quantization tutorial: Ref: Altland and Simons, Condensed Matter Field Theory Chapter 2.
Lecture 4 (Jan 28): Transverse Field Ising Model II (Solution)
Lecture 5 (Feb 2): Transverse Field Ising Model III - Experiment (Coldea et al., Science 2010).
Lecture 6 (Feb 4): Quantum to Classical Mapping Lecture 7 &8 (Feb 9, 11): D=2+1 Quantum Ising Model: Duality and Ising Gauge Theory (Ref: Wen pg 250, see bspace)
Lecture 9 (Feb 16): Deconfinement and Topological Order (Ref: Wen pg 252, see bspace)
Lecture 10&11 (Feb 18, 23): Insulating and Superfluid Phases in the Bose-Hubbard Model (Ref: Sachdev Chapter 10; Fisher et al. PRB 40, pg 546-550)
Lecture 13&14 (Mar 2, 4): Superfluid-Insulator Transition and Large-N (Ref: Sachdev Chapter 11, 5.2,5.3; Polyakov Chap. 8)
March 9&11 Special Lecture on Kitaev Models; Field Theory for Polymers
March 16 & 18 March Meeting. March 23 and 25: Spring Break. (no class)
Lecture 15 (Mar 30): Large-N final
Lecture 16 (Apr 1): Kosterlitz-Thouless Physics in D=1 Superfluid-Insulator system
Lecture 18&19 (April 8&13) Quantum Hall Effects (Review by Girvin)
Lecture 20&21 (April 15&20) Fractional Quantum Hall (Refs: Fractional Statistics Arovas; Composite Bosons: Zhang)
Lecture 22&23 (April 22&27) Chern Simons theory, topological order and edge states (Wen: Chapter 7.3) |