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Direct approaches to the quantum many-body problem suffer from the so-called"curse of dimensionality": the number of parameters needed to fully specify theexact wavefunction grows exponentially with increasing system size. Thismotivates the develop of accurate, but approximate, ways to parametrize thewavefunction, including methods like couple cluster theory and correlatorproduct states (CPS). Recently, there has been interest in approaches based onmachine learning both direct applications of neural network architecture andthe combinations of conventional wavefunction parametrizations with variousBoltzmann machines. While all these methods can be exact in principle, they areusually applied with only a polynomial number of parameters, limiting theirapplicability. This research's objective is to present a fresh approach towavefunction parametrization that is size-consistent, rapidly convergent, androbust numerically. Specifically, we propose a hierarchical ansatz thatconverges rapidly (with respect to the number of least-squares optimization).The general utility of this approach is verified by applying it touncorrelated, weakly-correlated, and strongly-correlated systems, includingsmall molecules and the one-dimensional Hubbard model.

A Size-Consistent Wave-function Ansatz Built from Statistical Analysis of Orbital Occupations