  We study the edge physics of gapped quantum systems in the framework of
Projected Entangled Pair State (PEPS) models. We show that the effective
low-energy model for any region acts on the entanglement degrees of freedom at
the boundary, corresponding to physical excitations located at the edge. This
allows us to determine the edge Hamiltonian in the vicinity of PEPS models, and
we demonstrate that by choosing the appropriate bulk perturbation, the edge
Hamiltonian can exhibit a rich phase diagram and phase transitions. While for
models in the trivial phase any Hamiltonian can be realized at the edge, we
show that for topological models, the edge Hamiltonian is constrained by the
topological order in the bulk which can e.g. protect a ferromagnetic Ising
chain at the edge against spontaneous symmetry breaking.
