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Sr$_{2}$IrO$_{4}$ has often been described via a simple, one-band pseudo-spin1/2 model, subject to electron-electron interactions, on a square lattice,fostering analogies with cuprate superconductors, believed to be well describedby a similar model. In this work we argue - based on a detailed study of thelow-energy electronic structure by circularly polarized spin and angle-resolvedphotoemission spectroscopy combined with dynamical mean-field theorycalculations - that a pseudo-spin 1/2 model fails to capture the fullcomplexity of the system. We show instead that a realistic multi-band HubbardHamiltonian, accounting for the full correlated $t_{2g}$ manifold, provides adetailed description of the interplay between spin-orbital entanglement andelectron-electron interactions, and yields quantitative agreement withexperiments. Our analysis establishes that the $j_{3/2}$ states make up asubstantial percentage of the low energy spectral weight, i.e. approximately74% as determined from the integration of the $j$-resolved spectral function inthe $0$ to $-1.64$ eV energy range. The results in our work are not only ofrelevance to iridium based materials, but more generally to the study ofmulti-orbital materials with closely spaced energy scales.

Constraints on the two-dimensional pseudo-spin 1/2 Mott insulator description of Sr$_2$IrO$_4$