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 (ES). Here we explore in depth this degeneracy for the spin-1 Affleck–Kennedy–Lieb–Tasaki 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 ES 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.

Haldane 相是自旋链系统的对称保护拓扑 (SPT) 相的原型。它可以受到几种对称性的保护，这些对称性具有纠缠谱 (ES) 的简并性。在这里，我们深入探讨了自旋 1 Affleck-Kennedy-Lieb-Tasaki 和双线性双二次哈密顿量的这种简并性，并展示了与周期链纠缠哈密顿量的低能量特性相关的体边缘对应的出现开链的物理哈密顿量。我们发现 ES 可以用两个自旋-1/2 作为开链末端的有效自旋来描述。在非连续分区的情况下，我们发现纠缠哈密顿量由自旋 1/2 海森堡哈密顿量给出，这表明了 SPT 相位和共形场理论之间的关系。我们最终研究了字符串顺序参数以及与块边对应关系的关系。