Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice

Understand

We construct a physically realistic and analytically tractable model for spin-1 systems with orbital degeneracy on the honeycomb lattice, relevant to honeycomb materials with large Hund's and weak spin-orbit couplings, and two electrons in t2g orbitals.

• This model realizes many new phases whose building blocks are orbital loops decorated by Haldane chains.
• These include a Haldane loop crystal, a symmetry-protected topological phase, and, notably, a regime where the decorated loops resonate.
• When taken to the three-dimensional hyperhoneycomb lattice, the latter regime becomes a (symmetry-enriched) U(1) quantum spin-orbital liquid, "disordered" both in the spin and orbital channels.