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Recent experiments show that the ground state of some of the layeredmaterials with localized moments is in close proximity to the Kitaev spinliquid, calling for a proper model to describe the measurements. TheKitaev-Hubbard model (KHM) is the minimal model that captures the essentialingredients of these systems, namely it yields the Kitaev-Heisenberg spin modelat the strong couling limit and contains the charge fluctuations present inthese materials as well. Despite its relevance, the phase diagram of the KHMhas not been rigorously revealed yet. In this work, we study the full phasediagram of the KHM using the $\mathbb{Z}_2$ slave-spin mean-field theory aswell as the auxiliary field quantum Monte Carlo (QMC) on rather large systemsand at low temperatures. The Mott transition is signaled by a vanishingquasiparticle weight evaluated using the slave-spin construction. Moreover, weshow using both QMC and slave spin approaches that there are multiple magneticphase transitions within the Mott phase including magnetically ordered phasesand most notably a spin liquid phase consistent with recent studies of the KHM.

Phase diagram of the Kitaev-Hubbard model: $\mathbb{Z}_2$ slave-spin and QMC approaches