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We present an approach to studying optical band gaps in real solids in whichquantum Monte Carlo methods allow for the application of a rigorous variationalprinciple to both ground and excited state wave functions. In tests thatinclude small, medium, and large band gap materials, optical gaps are predictedwith a mean-absolute-deviation of 3.5% against experiment, less than half theequivalent errors for typical many-body perturbation theories. The approach isdesigned to be insensitive to the choice of density functional, a property weexploit in order to provide insight into how far different functionals are fromsatisfying the assumptions of many body perturbation theory. We explore thisquestion most deeply in the challenging case of ZnO, where we show thatalthough many commonly used functionals have shortcomings, there does exist aone particle basis in which perturbation theory's zeroth order picture issound. Insights of this nature should be useful in guiding the futureapplication and improvement of these widely used techniques.

Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory