Iridate spin models: magnetism, 3D spin liquids and an infinite-D entanglement approximation

We present three-dimensional threefold-coordinated structures for iridates which may generate Kitaev-type magnetic exchanges. The resulting solvable 3D quantum spin liquid exhibits the uniquely 3D property of stability to finite temperature ($T_c \sim J_k/100$). Adding Heisenberg couplings spoils exact solubility; however, the large loop length $\ell$ of the lattice suggests an approximation with large $\ell \rightarrow \infty$. The Kitaev-Heisenberg model can be solved on the resulting Bethe lattice using tensor product states; we present the phase diagrams, finding multiple magnetic order parameters and identifying gapped spin liquid phases by an entanglement fingerprint.