The correspondence between the edge theory and the entanglement spectrum is firmly established for the chiral topological phases. We study a gapped, topologically ordered, nonchiral state with a conserved U(1) charge and show that the entanglement Hamiltonian contains not only the information about topologically distinct edges such a phase may admit, but also which of them will be realized in the presence of symmetry-breaking/-conserving perturbations. We introduce an exactly solvable, charge-conserving lattice model of a Z2 spin liquid and derive its edge theory and the entanglement Hamiltonian, also in the presence of perturbations. We construct a field theory of the edge and study its renormalization group flow. We show the precise extent of the correspondence between the information contained in the entanglement Hamiltonian and the edge theory. © 2017 American Physical Society.