A major advantage of variational Monte Carlo is the ability to use flexible and compact wave functions that otherwise would be difficult to evaluate the properties of without using Monte Carlo. This has resulted in a variety of wave function ansatze including multi-slater Jastrow, Pfaffians, backflow, and neural network based functional forms. However, it has been difficult to use these functional forms to describe excited states, either because the existing optimization algorithms can be unstable, or because orthogonalization to the ground state is done only on the determinant parameters. We show a penalty method which, unlike most penalty methods, does not require the limit of the penalty to infinity. We apply the method to several systems optimizing orbital, determinant, and Jastrow parameters independently for each state, and show that the method produces highly compact wave functions for the accuracy obtained. I will then describe a method we term density matrix downfolding to summarize the results from discrete excited states into effective models, which allows us to interpolate the QMC results to compute full spectra.
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