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The high-energy collective modes of particle-hole excitations across thespin-orbit gap in $\rm Sr_2IrO_4$ are investigated using the transformedCoulomb interaction terms in the pseudo-spin-orbital basis constituted by the$J=1/2$ and $3/2$ states arising from spin-orbit coupling. With appropriateinteraction strengths and renormalized spin-orbit gap, these collective modesyield two well-defined propagating spin-orbit exciton modes, with energy scaleand dispersion in excellent agreement with resonant inelastic X-ray scattering(RIXS) measurements.

Correlated motion of particle-hole excitations across the renormalized spin-orbit gap in $\rm Sr_2 Ir O_4$