Symmetry-protection in the deformed Affleck-Kennedy-Lieb-Tasaki state

The Haldane phase captured by the Affleck-Kennedy-Lieb-Tasaki (AKLT) state is a symmery-protected topological (SPT) phase protected by a set of symmetries: either inversion symmetry (IS), time-reversal symmetry (TRS) or the dihedral group of p rotations about two orthogonal axes (D2). This symmetry-protection follows from how the state transforms in its matrix product state (MPS) form under a certain symmetry operation.