A deep learning approach to quantum many-body physics with space group symmetries

Artificial neural networks (ANNs) have been utilized as an inexpensive wave function Ansatz together with quantum Monte Carlo (QMC) methods to solve quantum many-body systems. Such an approach has achieved success in solving 1D and 2D spin systems but also struggled with the exponential growth of complexity with respect to the size of the system. In order to overcome such an obstacle, the approach has to adopt network architectures and incorporate methods that perform effective dimensionality reduction and feature extraction. In this work, we demonstrate an ANN-QMC approach that uses a modified convolutional neural network architecture as the wave function Ansatz. We incorporate space group symmetry in the Monte Carlo sampling process to reduce system complexity. We test our approach on a fermionic model, the 2D Hubbard model on square lattices at half-filling, and approximate the ground state energy of the system.