Three times per week, 9-16 weeks.
M: 13:30-15:05 @402 Teaching BLDG
W: 15:20-16:55 @401 Teaching BLDG
F: 15:20-16:55 @403 Teaching BLDG
Office Hour: TBA
About the grade:
assignments (30%) + engagement (10%) + final exam (60%).
About the assignments:
Each assignment should be returned within one week. Overdue homework is not acceptable.
About this course:
This course is designed for senior undergraduate and graduate students in condensed matter physics, quantum many-body physics, and related fields. It assumes a basic background in quantum mechanics and statistical physics, with familiarity with linear algebra and introductory many-body physics helpful but not strictly required.
No prior knowledge of path integrals, topological phases, Chern–Simons theory, SU(N) spin systems, tensor-network methods, or nonequilibrium quantum dynamics is required. These topics will be developed from the necessary foundations throughout the course.
Course Outline:
Chapter 1 – Second Quantization
1.1 Bosonic Systems
1.2 Fermionic Systems
1.3 Spin Representation
1.4 Ferromagnetic Spin Waves
1.5 Antiferromagnetic Spin Waves
Chapter 2 – Path Integral
2.1 General Formalism
2.2 Bosonic Systems
2.3 Fermionic Systems
2.4 Spin Systems
2.5 Spin-Wave Description
Chapter 3 – Topology
3.1 Introduction
3.2 Nonlinear Sigma Models
3.3 Perturbative Expansion
3.4 Bosonic Topological States
3.5 Chern–Simons Theory
Chapter 4 – Symmetry-Protected Topological States
4.1 Spin-1 AKLT State
4.2 SU(N) Symmetry
4.3 SU(N) Topological States
4.4 iTEBD
4.5 Symmetry Analysis
4.6 Bosonic Chiral States
Chapter 5 – Nonequilibrium Topological States
5.1 Quantum Master Equations
5.2 Thermodynamic Topology
Assignments:
Suggested References:
[1] Altland A, Simons B. 凝聚态场论. 北京：世界图书出版公司，2012.
[2] Fradkin E. 凝聚态物理中的场论. 北京：世界图书出版公司，2013.
[3] Auerbach A. 相互作用电子和量子磁性. 北京：世界图书出版公司，2009.
[4] Negele J W, Orland H. Quantum Many-Particle Systems. Boulder: Westview Press, 1998.