Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model

TL;DR

This paper demonstrates that a q-deformed AKLT model exhibits symmetry-protected topological phase characteristics despite lacking standard protecting symmetries, due to an underlying quantum group symmetry.

Contribution

It introduces a new perspective on symmetry-protected topological phases beyond traditional symmetry groups, highlighting the role of quantum group symmetries in such phases.

Findings

Displays fractionalized boundary spins

Shows non-trivial string order

Exhibits entanglement spectrum degeneracy

Abstract

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-$\frac{1}{2}$ boundary spins, non-trivial string order and - when using an appropriate definition - a two-fold degeneracy in the entanglement spectrum. We trace these 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.