We address the role of non-local Coulomb correlations and short-range magnetic fluctuations in the high-temperature phase of Sr2IrO4 within state-of-the-art spectroscopic and first-principles theoretical methods. Introducing a novel cluster dynamical mean field scheme, we compute momentumresolved spectral functions, which we find to be in excellent agreement with angle-resolved photoemission spectra. We show that while short-range antiferromagnetic fluctuations are crucial to account for the electronic properties of the material even in the high-temperature paramagnetic phase, long-range magnetic order is not a necessary ingredient of the insulating state. Upon doping, an exotic metallic state is generated, exhibiting cuprate-like pseudo-gap spectral properties, for which we propose a surprisingly simple theoretical mechanism. arXiv:1801.08916v1 [cond-mat.str-el]
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