【主讲人】
Xu Yang (Ohio State University)
【摘要】
I will focus on the role of geometry and topology in quantum matter. In order to give students a flavor of the ubiquity of geometry and topology in physics, I will freely draw on mathematical tools in solving physics-motivated problems. Topics including crystalline defects, topological ordered states and tensor network states will be discussed. Mathematical tools of algebraic topology will be used extensively.
This short course will be lectures aiming at providing students with a perspective of the role of geometry and topology in condensed matter physics. Students with a general physics and math background (~level of sophomore) and a certain degree of mathematical maturity are encouraged to enroll.
【时间】
date：July 23rd/27th/29th/31st/, Aug 2nd/4th
time：09:00-10:00
【地点】
Room 412, Zhihua Building
【推荐读物】
Solid State Physics, N. Ashcroft and D. Mermin
Algebraic Topology, A. Hatcher
Geometric Phases in Physics, A. Shapere and F. Wilczek (ed.)
The density-matrix renormalization group in the age of matrix product states, U. Schollwoeck
【课程内容】
I will be focusing on the following topics:
1. Crystals and symmetry breaking
2. Distinction between metals and insulators: electric conductivity and beyond
3. Insulators (I): Lieb-Robinson bound and its manifestation in ground states and dynamics
4. Insulators (II): topological order in the tensor network formulation
5. Metals (I): Fermi surface, semiclassical dynamics
6. Metals (II): quantum geometry
【作业】
There will be one homework problem per lecture to help students get familiar with ideas and calculations.
