Deep learning-enhanced variational Monte Carlo method for quantum many-body physics

Artificial neural networks have been successfully incorporated into the variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies exploring quantum many-body physics using deep neural networks (DNNs), despite the tremendous success enjoyed by DNNs in many other areas in recent years. One main challenge of implementing DNNs in VMC is the inefficiency of optimizing such networks with a large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNNs by VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional SU(N) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNNs show excellent agreement with the Bethe ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum many-body calculations.