Abstract
A topological phase is a phase of matter which cannot be characterized by a local order parameter. We introduce non-local order parameters that can detect symmetry protected topological (SPT) phases in 1D systems and then show how to generalize the idea to detect certain symmetry enriched topological (SET) phases in 2D. The proposed approaches are particularly useful if the quantum states are represented in terms of tensor product states. As concrete examples, we examine two model states which exhibit SET order: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond state on a kagome lattice.