Special Topics: Solid State Physics (P897), Spring 2023

Special Topics: Solid State Physics (P897), Spring 2023

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

Lectures: TuThu 10.00-11.15am, room: Has 136

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://websites.umass.edu/rvasseur/teaching/. See slack channel for class updates.

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

Topics:

  • 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: See Slack.

Final Exam: 

Schedule: 

  • 2/7: Introduction, transverse field Ising model, symmetry. Chap 1, Chap 2: pages 1-2.
  • 2/9: Quantum Ising chain: phases and excitations, spontaneous symmetry breaking. Chap 2: pages 3-6.
  • 2/14: Domain walls, KW duality, Majorana fermions. Chap 2: pages 7-10.
  • 2/16: Majorana fermions cont’d, Hamiltonians, phases and Majorana edge modes. Chap 2: pages 11-13.
  • 2/21: TF Ising model: Exact solution. Quantum to classical mapping in 0d. Chap 2: pages 14-15. Chap 3: pages 1-2.
  • 2/23: Quantum-to-classical correspondence, finite T and T=0 universality classes. Chap 3: pages 3-6.
  • 2/28: Continuum limit of the TFIM, Majorana field theory, equations of motion. Chap 4: pages 1-3.
  • 3/2: Relativistic Majorana equation, Fermionic coherent states and Grassmann variables. pages 4-6.
  • 3/7: Kitaev chain, domain wall and Majorana zero mode in continuum picture. End fermionic functional integral. Chap 3: appendix on Kitaev chain. Chap 4: page 7.
  • 3/9: Majorana field theory, Lagrangian and scale invariance. Chap 4: pages 8-10. Chap 5: page 1.
  • 3/21: Conformal invariance, finite T correlators, primary operators. Wilsonian RG. Chap 5: pages 2-6.
  • 3/23: RG cont’d. Irrelevant operators, Majorana CFT fixed point and universality. Chap 5: pages 7-10.
  • 3/30: Free fermion CFT. Chap 6: pages 1-4.
  • 3/31: Free boson CFT. Chap 6: pages 5-7.
  • 4/4: Vertex operators, compactification. Chap 6: pages 8-11.
  • 4/6: Compact boson CFT. Start bosonization. Chap 6: pages 11-14.
  • 4/11: Bosonization, dictionary. Chap 6: pages 14-16.
  • 4/13: Bosonization of the XXZ spin chain. Chap 6: pages 17-20.
  • 4/20: Bosonization of the XXZ spin chain cont’d. Chap 6: pages 20-23.


Solutions available on Slack channel

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