Effective spin-orbit models using correlated first-principles wave functions

In recent years, spin-orbit effects have been used to design and predict new emergent phases in condensed matter systems. Most of the theory has been done at the level of band structure. It is of high current interest how to extend these ideas to correlated electron systems. We present a new computational technique that uses first-principles quantum Monte Carlo calculations to address spin-orbit effects efficiently while also treating electron correlation accurately. To test this technique, we perform benchmark calculations in atomic systems and monolayer tungsten disulfide. The calculated results of the spin-orbit splittings in these systems agree with the experimentally determined values. This new tool allows us to investigate electron-electron interaction, spin-orbit effects and one-body terms on the same footing in realistic materials, with a cost similar to the standard fixed-node diffusion Monte Carlo.