Insights into correlated electron systems from first-principles quantum Monte Carlo

Accurate first-principles calculations can provide valuable predictions for material-specific properties as well as simplified models for interpreting materials' behavior. However, the level of accuracy required is difficult to reach in systems where it is important to properly account for electron correlations. I report several benchmarks establishing that variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (FN-DMC) are efficient enough to compute properties of realistic systems while significantly improving on the accuracy of more commonly-used first-principles approaches. For chemical reactions, FN-DMC can provide reaction barrier estimates that have reached ``chemical accuracy,'' the accuracy threshold to predict room-temperature chemistry measurements. For the iron-based superconductor, FeSe, I report on quantum Monte Carlo calculations that accurately reproduce the structural properties, including the lattice constants and the equation-of-state. In FeSe, I also found a coupling between the structure, spin texture, and orbital occupation in the system that may be relevant to explain some of the unique properties of that system. To establish its predictive capabilities, I also utilize FN-DMC to make a prediction for the singlet-triplet gap of MgTi2O4, a spinel system relevant to the search for spin liquids. We found that the gap was larger than previous experiments have considered, and may explain why the singlet-triplet gap has not yet been observed in that system. In addition to calculating material properties, I also leverage FN-DMC to characterize systems using simple models. In FeSe, starting from the assumption that Hund's coupling is important, I found a simple model that was able to explain how the electronic properties varied with spin texture. Using a downfolding procedure combined with FN-DMC and tools from data science, I analyzed the importance of a wide class of effective model terms in describing an Fe-Se diatomic molecule. The study determined that Hund's coupling was the most important interaction in this system, and quantified its importance relative to other terms. I also developed a new strategy for efficiently discovering low-energy states in the Hilbert space, an important input for developing low-energy effective models. I applied this strategy in H2 in two geometries where a tight-binding model is accurate and where it breaks down, and I quantify the importance of interactions in the effective model. The results establish the accuracy of FN-DMC for correlated electron systems and develop strategies for determining accurate effective lattice models from first-principles quantum Monte Carlo