Modeling multiorbital effects in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>IrO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> under strain and a Zeeman field

We present a comprehensive study of three-orbital lattice model suitable for the layered iridate ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. Our analysis includes various on-site interactions (including Hubbard and Hund's) as well compressive strain, Zeeman magnetic field. use self-consistent mean-field approach with multiple order parameters to characterize resulting phases. While in some parameter regimes compound is described by an effective $J=1/2$ model, other regimes, full multiorbital description needed. As function we uncover two quantum phase transitions: first continuous metal-insulator transition, subsequently first-order melting antiferromagnetic order. Crucially, bands both $J=3/2$ nature play important roles these transitions. results qualitatively agree experiments ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ under strain induced substrate motivate higher strains.