Recently, there has been significant progress in solving quantum many-particle problems via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this paper, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, solving the highly frustrated spin-1/2 $J_1-J_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.

• Received 24 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.104426