PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Stephanie Zerby.

Title:Classifications of symmetry protected topological phases in interacting boson/fermion systems
Seminar:Noncommutative Geometry Seminar
Speaker:Zhengcheng Gu, Perimeter Institute
Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory. However, it is not known what SPT phases exist in general interacting systems. In this talk, I will first present a systematic way to construct SPT phases in interacting boson systems, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimensions and one in two dimensions protected by particle number conservation and time reversal symmetry. Just like group theory allows us to construct 230 crystal structures in 3D, we find that group cohomology theory allows us to construct different interacting bosonic SPT phases in any dimensions and for any symmetry groups. In particular, I am going to show how topological terms in the path integral description of the system can be constructed from nontrivial group cohomology classes, giving rise to exactly soluble Hamiltonians, explicit ground state wavefunction. If time is allowed, I will discuss the generalization of the classifying scheme for interacting fermion/electron systems and propose a new mathematical framework – group supercohomology theory, which predicts a novel fermionic SPT phase that can neither be realized in free fermion systems nor in interacting boson systems.

Room Reservation Information

Room Number:MB114
Date:02 / 12 / 2015
Time:02:30pm - 03:30pm