Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain and the associated quantum group invariant AKLT model

We argue that the q-deformed spin-1 AKLT Hamiltonian should be regarded as a representative of a symmetry protected topological phase. Even though it fails to exhibit any of the standard symmetries known to protect the Haldane phase it still displays all characteristics of this phase: Fractionalized spin-1/2 boundary spins, non-trivial string order and - when using an appropriate definition - a two-fold degeneracy in the entanglement spectrum. Numerical computations using iDMRG show that these features also persist in parts of the phase diagram of the q-deformed bilinear-biquadratic spin chain whose structure is analyzed in detail.

We trace the topological properties back to the existence of an SO_q(3) quantum group symmetry and speculate about potential links to discrete duality symmetries. We expect our findings and methods to be relevant for the identification, characterization and classification of other symmetry-protected topological phases with non-standard symmetries.