A major challenge in condensed matter physics, chemistry, and materials is to be able to compute the properties of electrons in real materials. Auxiliary field quantum Monte Carlo is a promising numerical method for these systems. It is proven to be highly accurate and be able to treat large number of electrons in the Simons many-electron collaboration. We apply the state of art auxiliary field quantum Monte Carlo for realistic transition metal systems. The many-body ab initio Hamiltonian is treated directly on transition metal atoms, their ions, and their monoxide molecules. We show ionization energy and dissociation energy on transition metal systems are indistinguishable from experimental results. Then, we studied the low temperature phase diagram of Ca2RuO4 for a range of layered perovskite structures. Our calculations find that the metal-insulator transition in Ca2RuO4 is driven by a structural transition from a long c-axis to a short c-axis perovskite in this material and is accompanied by a ferromagnetic-antiferromagnetic transition. Our many-body simulations capture the phase diagram and explain the origin of the magnetic and metal-insulator transitions in Ca2RuO4.
