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