Topological Quantum Matter (Independence 2025)

Logistics: 

Metting time: Fridays 15:30 pm, Room 314

Overview of course

This reading course will be on introduction to the notion of topological phases from a modern point of view. We will mainly focus on the simplest of these, called 'invertible phases of matter' which includes quantum Hall states, topological insulators and so on

Topics to be covered:

1. Precisely defining gapped phases of matter

2. Example: Haldane chain

3. Topological band theory

4. Symmetries and their representations

5. Group cohomology SPT phases

6. Understanding through field theory

7. Mathematical structure 

References

There will be no standard refrerence because no reference exists. I have provided a partial list below which I will add to as the course progresses. 

1. https://boulderschool.yale.edu/2016/boulder-school-2016

2. https://static.ias.edu/pitp/2015/schedule.html

3. Topological insulators and topological superconductors, book Taylor Hughes and Andrei Bernvig

4. Topological band theory and the Z2 invariant

5. NPTEL Lectures by Prof. Sourabh Basu