Condensed Matter Seminar: Hassan Shapourian, University of Chicago - “Topological invariants and entanglement in SPT phases of fermions “

Searching for a proper set of order parameters which distinguish different phases of matter sits in the heart of condensed matter physics. In this talk, I discuss topological invariants as (non-local) order parameters of symmetry protected topological (SPT) phases of fermions in the presence of anti-unitary symmetries. I introduce a general framework to construct topological invariants in terms of expectation values of some operators, where the role of the operator can be viewed as twisting by symmetry. In the case of time-reversal symmetry, it turns out that the operation of twisting by symmetry is partial transpose. The partial transpose can then be used to define an intrinsic measure of entanglement in fermionic systems. Throughout the talk, I take one dimensional time-reversal symmetric topological superconductors (class BDI) as an example and explain how the above ideas work.