Fall 2019

Physics 268r: Special Topics in Quantum Matter


This is a special topics course on quantum systems of many particles, i.e. quantum matter. We will study well defined microscopic models, such as simple spin models, representing electrons in solids or atoms in optical lattices, which will be shown to give rise to remarkable new excitations, from `sound’ and `light’, to fermions and even more exotic `anyon’ excitations. Often, (but not always) we will use field theory to describe this physics, which may also help demystify the origin of quantum field theory in a physical setting free from `infinities’.

This course will make contact with recent research directions such as topological order, quantum criticality and dualities

An earlier version of this course can be found here

(r, t) = (in Lyman 425, Friday 12:00pm-2:45pm SINGLE CLASS per week for 2:45 mins with a break)

Prerequisites: Previous offerings of this course have been taken mainly by condensed matter/AMO and high energy theory graduate students, although the only real requirements are a strong background in quantum mechanics and statistical mechanics. Some exposure to critical phenomena and renormalization group ideas will be helpful.

Planned Topics:

1.The 1+1D transverse field Ising model - duality, fermionization, chiral symmetry. Experimental realization of “E8” in   CoNb2O6. 

2. Continuous symmetry breaking in 2+1D. Goldstone modes and the Anderson Tower. Non-perturbative approaches such as dualities and large-N expansions. The Mott-superfluid transition in optical lattices.

3. Emergent Gauge Theories and topological order. Confinement and topological order. Chern Simons theories. Fractional quantum Hall states and gapped quantum spin liquids. Emergent electromagnetism in quantum magnets and “Spin-ice”.

4. Special Topics: Quantum entanglement in many body systems. Scale invariance.


Assignments (roughly biweekly) and a final reading/small research project in groups of 2-3 based on enrollment. There will be no examinations.

Suggested Text 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


Previous Courses

  • Physics 181 (Statistical Mechanics). 
  • Phy211 (Spring 2016) 'Statistical Mechanics'
  • Phy212 (Fall 2015) 'Advanced Statistical Mechanics'
  • Phy216 (Fall 2014) 'Quantum Magnetism & Strongly Correlated Electronic Systems'
  • Phy 250 (Fall 2013)  'Demystifying Quantum Field Theory'

Les Houches 2014 Lecture Notes: