  The Haldane phase is the prototype of symmetry protected topological (SPT)
phases of spin chain systems. It can be protected by several symmetries having
in common the degeneracy of the entanglement spectrum. Here we explore in depth
this degeneracy for the spin-1 AKLT and bilinear-biquadratic Hamiltonians and
show the emergence of a bulk-edge correspondence that relates the low energy
properties of the entanglement Hamiltonian of a periodic chain and that of the
physical Hamiltonian of an open chain. We find that the entanglement spectrum
can be described in terms of two spins-1/2 behaving as the effective spins at
the end of the open chain. In the case of non-contiguous partitions, we find
that the entanglement Hamiltonian is given by the spin-1/2 Heisenberg
Hamiltonian, which suggests a relationship between SPT phases and conformal
field theory. We finally investigate the string order parameter and the
relation with the bulk-edge correspondence.
