Theory Seminar: Irreducible projective representations and their physical applications

Zheng-Xin Liu (Renmin University of China)
In the first part of the talk, we apply the eigenfunction method to obtain all irreducible projective representations (Reps) of finite groups, especially anti-unitary groups

Zheng-Xin Liu (Renmin University of China)
Herbert-Walther Lecture Hall G0.25
Special Theory Group Seminar at 13:45

Abstract:

In the first part of the talk, we apply the eigenfunction method to obtain all irreducible projective representations (Reps) of finite groups, especially anti-unitary groups. To this end, we first solve the cocycle equations to obtain the factor system of each class of projective Rep, from which we construct the regular projective Rep. Then we use the eig-values of class operators to label the bases of each irreducible Rep. In the second part, we discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as the Dirac semimetals in Magnetically ordered systems.