Excited State Variational Principles for Real Solids

We will present recent progress on the adaptation for solid state applications of variational Monte Carlo methods that optimize wave functions directly for excited states. These methods are based on rigorous variational principles that allow an interior eigenstate of the Hamiltonian to be targeted directly based on its location in the spectrum in direct analogue to how the traditional variational principle targets the ground state. In combination with recent progress in Monte Carlo wave function optimization techniques, such methods offer a new opportunity in modeling the optical band gaps of real materials. In particular, the systematic improvability and non-perturbative nature of the approach makes it especially appealing in the context of strongly correlated materials, for which current many-body methods face substantial difficulties.