Condensed Matter Physics Seminar

Symmetry protected topological (SPT) states are distinct from trivial product states so long as the symmetry is preserved, but no local order parameter can detect the nature of the order. Given a microscopic Hamiltonian, how can we determine if the ground state has SPT order?  I'll first review the solution for SPTs in 1d, focusing on how the physical responses to flux insertion can be related to the rather abstract group cohomology formalism. Proceeding to two dimensions, SPTs have two observable responses to flux insertion: flux binds fractional charge, and flux can bind a degeneracy which transforms projectively under the symmetry. Both responses can be determined by a simple (but non-local) measurement on the ground state of a cylinder. Finally, I will relate the flux responses to the cohomology classification, and show they give a complete characterization for finite abelian symmetry groups.