Three-dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite- D approximation.

Motivated by the recent synthesis of two insulating Li2IrO3 polymorphs, where Ir4+ Seff = 1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting β-Li2IrO3 hyperhoneycomb lattice and γ-Li2IrO3 stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90° Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z2 flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with Tc ≈ ∣ K ∣ /100. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop l is relatively large in these structures, we construct an l → oo approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint. [ABSTRACT FROM AUTHOR]