Hidden orders and flux attachment in symmetry protected topological phases

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, a hidden order parameter exists and constitutes the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in symmetry protected topological phases (SPTs) is a largely open question, especially in 2D and 3D. In this talk I will introduce a new approach to analyzing SPT groundstates, based on generalized Laughlin wavefunctions. Using it one obtains a simple picture of some classes of SPTs in 1D and 2D, in which hidden order is rather explicit. Future directions, in the lines of generalizing the composite-particle approach to SPTs, will be discussed briefly.