LAUSR

Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state-of-the-art many-body methods, auxiliary field quantum Monte Carlo and dynamical mean field theory, to determine the low-temperature phase diagram of ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$. Both methods predict a low-temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. The properties of the ferromagnetic state vary nonmonotonically with pressure and are dominated by the ruthenium ${d}_{xy}$ orbital, while the properties of the antiferromagnetic state are dominated by the ${d}_{xz}$ and ${d}_{yz}$ orbitals. Differences in the details of the predictions of the two methods are analyzed. This work is theoretically important as it presents the first application of the auxiliary field quantum Monte Carlo method to an orbitally degenerate system with both Mott and Hunds physics and provides an important comparison of the dynamical mean field and auxiliary field quantum Monte Carlo methods.