How to Make Compact Wave Functions on the Cheap: Stochastic Variational Algorithms for Quantum Physics and Chemistry

Most many body methods for solving the electronic Schrodinger Equation require a reasonable starting point -- a respectable trial wave function -- in order to achieve the chemical accuracy necessary to make reliable predictions about molecular and material properties. Currently, most electronic structure methods use low accuracy mean field theory or simple variational techniques to produce such wave functions. In this talk, I will discuss the applied mathematics behind a suite of new methods my group has recently developed to produce high accuracy, correlated variational wave functions that can be used with Fock space methods such as Auxiliary Field Quantum Monte Carlo or other common quantum chemistry techniques. I will demonstrate how these methods scale and perform on a variety of lattice models and end with a discussion of how tricks from renormalization group theory can be used to generalize our approach to treat molecules and materials.