  It is well known that the bulk physics of a topological phase constrains its
possible edge physics through the bulk-edge correspondence. Therefore, the
different types of edge theories that a topological phase can host constitute a
universal piece of data which can be used to characterize topological order. In
this paper, we argue that, beginning from only the fixed-point wave function
(FPW) of a nonchiral topological phase and by locally deforming it, all
possible edge theories can be extracted from its entanglement Hamiltonian (EH).
We give a general argument, and concretely illustrate our claim by deforming
the FPW of the Wen-plaquette model, the quantum double of $\mathbb{Z}_2$. In
that case, we show that the possible EHs of the deformed FPW reflect the known
possible types of edge theories, which are generically gapped, but gapless if
translational symmetry is preserved. We stress that our results do not require
an underlying Hamiltonian--thus, this lends support to the notion that a
topological phase is indeed characterized by only a set of quantum states and
can be studied through its FPWs.
