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

TL;DR

This paper introduces a size-consistent, rapidly convergent wavefunction ansatz based on statistical analysis of orbital occupations, applicable to various correlated quantum systems, improving efficiency and robustness over traditional methods.

Contribution

It presents a novel hierarchical wavefunction ansatz that is size-consistent, converges quickly, and is robust, demonstrated on molecules and the Hubbard model.

Findings

Achieves rapid convergence with fewer parameters.

Demonstrates applicability to diverse quantum systems.

Shows improved numerical stability and size-consistency.

Abstract

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.