Special Topics: Solid State Physics (P897), Spring 2019
Instructor: Romain Vasseur, Assistant Professor
office: Hasbrouck 405A
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
- 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.
- Transverse Field Ising Chain
- Quantum-Classical Correspondence
- Majorana Field Theory
- Scale Invariance and RG
- Bosonization and Luttinger Liquids
- Gauge theories
- Jordan Wigner Transformation & Kitaev Chain
- Quantum-to-Classical mapping, XXZ spin chain & Dirac Fermions
- Luttinger Liquids
Final Exam: Exam
Solutions available on Moodle, or upon request by email.