Approximating quantum many-body wave-functions using artificial neural networks

In this talk, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-driven complex sign rule in the ground state. The practical application of this method to explore the unknown ground states is also discussed.
Zi Cai, arXiv:1704.05148 (2017)