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

Abstract

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 π 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. We study the q-deformed AKLT (AKLT_q ) state which also has a known MPS form that continuously transforms to that of an AKLT state and how this symmetry-protection is altered. We show that the AKLT_q state can be adiabatically connected to the AKLT state when IS is protected. However, our approach does not conclusively lead to the similar conclusion for TRS and D₂ , hence, we discuss possible explanations.