Condensed matter physics is rather unique in that we know the high-energy theory nearly exactly(quantum mechanics of nuclei and electrons) but solving the Schroedinger equation accurately enough to address the low energy physics is very challenging, primarily because of electron correlation . Progress can be made using numerical methods such as variational quantum Monte Carlo (VMC), which allows for explicitly correlated and flexible wave functions, including recently neural network ansatzes. However, historically VMC methods have been limited to ground state calculations only.

I will present a new ensemble variational principle for the lowest N eigenstates of an arbitrary Hamiltonian. I show that this principle allows us to derive a new optimization algorithm for excited states, and is scalable for first principles models of condensed matter systems. I will present some new results on strongly correlated systems along with comparisons to traditional embedding methods.