  In this paper, 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-induced complex sign rule in the ground state and approximates
the ground states with high precisions. As an example of practical use of our
method, we also perform the variational method to explore the ground state of
an anti-ferromagnetic $J_1-J_2$ Heisenberg model.

Strongly Correlated Electrons