Using ab initio methods for correlated electrons in solids, we investigate the metal-insulator transition across the Ruddlesden-Popper (RP) series of iridates and explore the robustness of the Jeff=1/2 state against band effects due to itineracy, tetragonal distortion, octahedral rotation, and Coulomb interaction. We predict the effects of epitaxial strain on the optical conductivity, magnetic moments, and Jeff=1/2 ground-state wave functions in the RP series. To describe the solution of the many-body problem in an intuitive picture, we introduce a concept of energy-dependent atomic states, which strongly resemble the atomic Jeff=1/2 states but with coefficients that are energy or time dependent. We demonstrate that the deviation from the ideal Jeff=1/2 state is negligible at short time scales for both single- and double-layer iridates, while it becomes quite significant for Sr3Ir2O7 at long times and low energy. Interestingly, Sr2IrO4 is positioned very close to the SU(2) limit, with only ∼3% deviation from the ideal Jeff=1/2 situation.
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