Special Topics: Solid State Physics (P897), Spring 2019

Special Topics: Solid State Physics (P897), Spring 2019

Instructor: Romain Vasseur, Assistant Professor
office: Hasbrouck 405A
email: rvasseur[at]umass[dot]edu
office hours: by appointment and email, or visit my office

Lectures: TuThu 2.30-3.45am, room: Has 104A

Suggested reading materials:

  • “Quantum Phase Transitions”, Subir Sachdev (Cambridge University Press). 
  • “Field Theories of Condensed Matter Physics”, Eduardo Fradkin (Cambridge University Press).
  • “Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons”, Xiao-Gang Wen (Oxford Graduate Texts). 
  • “Quantum Field Theory and Condensed Matter: An Introduction”, Ramamurti Shankar (Cambridge Monographs on Mathematical Physics).

Website: https://blogs.umass.edu/rvasseur/teaching/. Course materials will also be made available on Moodle.

Grading: The course grade will be based on the problem sets (65%), and a take-home exam (35%). 


  • Introduction: QFT, cutoffs and universality
  • Transverse field Ising model: phases and excitations, Jordan-Wigner transformation, duality and Majorana fermions. Kitaev chain and Majorana edge modes
  • Quantum-classical correspondence 
  • Majorana field theory
  • Scaling and a (very) brief introduction to the Renormalization Group
  • Bosonization and Luttinger liquids 
    • Free fermion and free boson CFT
    • Bosonization
    • Luttinger liquids
  • Discrete gauge theory and topological order: 
    • 2+1d Ising duality and Z_2 Gauge theory
    • Deconfinement and Abelian topological order
    • Anyons and Toric code
  • Time Permitting: U(1) Spins and superfluidity, Superfluid-Mott insulator transition, Topological defects and particle-vortex duality.

Lecture Notes:

  1. Introduction
  2. Transverse Field Ising Chain
  3. Quantum-Classical Correspondence
  4. Majorana Field Theory
  5. Scale Invariance and RG
  6. Bosonization and Luttinger Liquids
  7. Gauge theories

Problem Sets:

  1. Jordan Wigner Transformation & Kitaev Chain
  2. Quantum-to-Classical mapping, XXZ spin chain & Dirac Fermions
  3. Luttinger Liquids

Final Exam: Exam

Solutions available on Moodle, or upon request by email.

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