Boulder School 2016: Lecture Notes

Week 1: July 11-15

Quantum Hall Effect I

Background Reading:

• N. Read, “Topological phases and quasiparticle braiding”, Physics Today: 38-43 (July 2013)
• N. Read & D. Green, “Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect”, Physical Review B61: 267-297 (2000)

Student Notes

Effective Field Theories of Topological Phases & Quantum Computation I

Background Reading:

• M. Freedman, C. Nayak, K. Shtengel, K. Walker, and Z. Wang, “A class of P, T-invariant topological phases of interacting electrons”, Annals of Physics 310: 428-492 (2004)
• A.Yu. Kitaev, “Fault-tolerant quantum computation by anyons”, Annals of Physics 303: 2-30 (2003)
• J. Cano, M. Cheng, M. Mulligan, C. Nayak, E. Plamadeala, and J. Yard, “Bulk-Edge Correspondence in 2 + 1-Dimensional Abelian Topological Phases”, Preprint
• C. Nayak, S.H. Simon, A. Stern, M. Freedman, and S. Das Sarma, “Non-Abelian Anyons and Topological Quantum Computation”, Preprint

Student Notes

Topological Insulators I

Background Reading:

• M.Z. Hasan & C. Kane, “Colloquium: Topological Insulators”, Reviews of Modern Physics 82: 3045-3067 (2010)
• C. Kane, Topological Band Theory and the Z2 Variant (Chapter one)

Homework

Student Notes

Quantum Hall in Graphene & Beyond I

Presentation

Student Notes

Entanglement I

Background Reading:

• Table of Contents
• Book section
• Entanglement readings

Student Notes

Week 2: July 18-22

Classification of Topological Insulators I

Supporting Reference

Weyl semimetals & SPT phases I

Supporting References

Student Notes

Majoranas I

Additional Notes

Notes 3

Notes 4

Topological Superconductors I

Slides

Student Notes

Week 3: July 25-29

Spin Liquids I

Student Notes

Majoranas in Nanowires I

Homework

Tensor Network Methods for Spin Liquids I

Supporting Reference

Public Lecture: "Strange Stuff: A Second Quantum Revolution"

Poster

SPT & SET Phases I

Reference Material

Student Notes

Topological State Numerics

Slides

Week 4: August 1-5

2 & 3D Topological Phases I

References:

• Levin and Wen, String-net condensation: A physical mechanism for topological phases
• Kitaev and Kong, Models for gapped boundaries and domain walls
• Bravyi and Kitaev, Quantum codes on a lattice with boundary
• Wang and Levin, Braiding statistics of loop excitations in three dimensions

Student Notes