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The Haldane phase is the prototype of symmetry protected topological (SPT)phases of spin chain systems. It can be protected by several symmetries havingin common the degeneracy of the entanglement spectrum. Here we explore in depththis degeneracy for the spin-1 AKLT and bilinear-biquadratic Hamiltonians andshow the emergence of a bulk-edge correspondence that relates the low energyproperties of the entanglement Hamiltonian of a periodic chain and that of thephysical Hamiltonian of an open chain. We find that the entanglement spectrumcan be described in terms of two spins-1/2 behaving as the effective spins atthe end of the open chain. In the case of non-contiguous partitions, we findthat the entanglement Hamiltonian is given by the spin-1/2 HeisenbergHamiltonian, which suggests a relationship between SPT phases and conformalfield theory. We finally investigate the string order parameter and therelation with the bulk-edge correspondence.

Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian