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Using ab-initio methods for correlated electrons in solids, we investigatethe metal-insulator transition across the Ruddlesden-Popper (RP) series ofiridates and explore the robustness of the J_eff=1/2 state against band effectsdue to itineracy, tetragonal distortion, octahedral rotation and Coulombinteraction. We predict the effects of epitaxial strain on the opticalconductivity, magnetic moments, and J_eff=1/2 ground-state wave functions inthe RP series. To describe the solution of the many-body problem in anintuitive picture, we introduce a concept of energy-dependent atomic states,which strongly resemble the atomic J_eff=1/2 states but with coefficients thatare energy/time-dependent. We demonstrate that the deviation from the idealJ_eff=1/2 state is negligible at short time scales for both single- anddouble-layer iridates, while it becomes quite significant for Sr3Ir2O7 at longtimes and low energy. Interestingly, Sr2IrO4 is positioned very close to theSU(2) limit, with only 3% deviation from the ideal J_eff=1/2 situation.

Effective J=1/2 insulating state in Ruddlesden-Popper iridates: An LDA+DMFT study