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The two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling (Si - Sj)n, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multiorbital Mott insulators. We focus on t2g electrons on the honeycomb lattice and propose a physical realization of the spin-3/2 AKLT state. We find a phase transition from the AKLT to the Neel state on increasing Hund's rule coupling, which is confirmed by density matrix renormalization group simulations. An experimental signature of the AKLT state consists of protected, free 5 = 1/2 spins on lattice vacancies, which may be detected in the spin susceptibility. [ABSTRACT FROM AUTHOR]

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2Ir03 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from &thetas; = --125 K for Na2Ir03 to &thetas; ≈ --33 K for Li2Ir03, while the ordering temperature remains roughly the same TN ≈ 15 K. Using functional renormalization group calculations we show that this evolution of &thetas; and TN as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2Ir03 is deep in a magnetically ordered regime, while Li2Ir03 appears to be close to a spin-liquid regime. [ABSTRACT FROM AUTHOR]