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Hole propagation in the Kitaev-Heisenberg model: From quasiparticles in quantum Neel states to non-Fermi liquid in the Kitaev phase

We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the t-J-like Kitaev-Heisenberg model on a honeycomb lattice: the Neel antiferromagnetic, stripe, zigzag and Kitaev spin-liquid phase. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a similar mechanism as in the $t$-$J$ model for high-$T_c$ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely {\it hidden} in those spectral functions that correspond to photoemission experiments. As the most surprising result, we find a totally incoherent spectral weight distribution for the spectral function of a hole moving in the Kitaev spin-liquid phase in the strong coupling regime relevant for iridates. At intermediate coupling the finite systems calculation reveals a well defined quasiparticle at the $Γ$ point, however, we find that the gapless spin excitations wipe out quasiparticles at finite momenta. Also for this more subtle case we conclude that in the thermodynamic limit the lightly doped Kitaev liquid phase does not support quasiparticle states in the neighborhood of $Γ$, and therefore yields a {\it non-Fermi liquid}, contrary to earlier suggestions based on slave-boson studies. These observations are supported by the presented study of the dynamic spin-structure factor for the Kitaev spin liquid regime.