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

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 $S{O}_q(3)$ 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.

arXiv comment8 pages, v2: Added some discussion on qAKLT states based on higher auxiliary spins and their entanglement properties, v3: Changed title to conform to journal guidelines, moved one section from the appendix to the main text and added more comments and references concerning twisted boundary conditions. Version as submitted to and accepted in Phys Rev B as a Rapid Communication (Editors' Suggestion)

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