Solving quantum many-body problems by combining artificial neural network with variational Monte Carlo

Artificial neural networks have been successfully incorporated with variational Monte Carlo (VMC) to study quantum many-body problems. In this study, we propose a modified neural network architecture to represent ground-state wave functions, using separate convolutional channels of different widths and depths for the amplitude and phase of the wave function. A Hamiltonian matrix tree search and importance sampling VMC are used to improve the efficiency of the Markov chain sampling for gradient-based optimization of the ground-state energy. Space group symmetry of the lattice is also included to reduce the computational complexity and obtain quantum many-body states at a given k point. This framework is demonstrated by computing the ground-state energy of strong interacting quantum spin models.