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

TL;DR

This paper introduces a new spin-orbital model on the honeycomb lattice that predicts novel quantum phases, including topological and spin-liquid states, relevant to certain honeycomb materials with orbital degeneracy.

Contribution

It presents an analytically tractable model capturing orbital loop states decorated by Haldane chains, leading to various exotic phases including a U(1) quantum spin-orbital liquid.

Findings

Discovery of a Haldane loop crystal phase.

Identification of a symmetry-protected topological phase.

Prediction of a U(1) quantum spin-orbital liquid in 3D.

Abstract

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. We hope this construction will pave the way for realizing many of the Haldane-chain-based phases which have been theoretically proposed in the literature.