Group cohomology and algebraic topology as the mathematical theory for Symmetry protected topological order in physics

TitleGroup cohomology and algebraic topology as the mathematical theory for Symmetry protected topological order in physics

 

SpeakerXiao-Gang Wen Dept. of Physics, MIT

 

Time:  12:00-17:00 pm, December 24, 2014

14:00--15:20  Lecture One

15:20--15:40  Tea Time

15:40--17:00  Lecture Two

Place Cheng yu-tung lecture hall

 

Abstract

Symmetry protected topological (SPT) states are a new kind of quantum states of matter, which are beyond Landau symmetry breaking theory and cannot be described by group theory. As new state of matter, SPT states have many new properties, such as non-trivial gapless boundary and point defects with fractional statistics. In these two lectures, I will present

(1) a systematic theory of SPT order based on non-linear sigma model and its topological terms, which turns out to be a group cohomology theory

(2) ways to probe/measure SPT orders, and the connection to gauge/gravitational anomalies, which turns out to be an algebraic topology theory

(3) mechanism to generate SPT orders