Self-learning Monte Carlo Method with Deep Neural Networks*

Self-learning Monte Carlo (SLMC) method is a general algorithm to speedup MC simulations. Its efficiency has been demonstrated in various systems by employing the effective model to propose global moves in configuration space. Here, we explicitly show that deep neural networks can be naturally embedded in SLMC as the effective model, and further extend the realm of SLMC. Without any prior physical knowledge, the neural network could accurately learn the dynamics of the original model in a quantitatively level. By extracting physical information from the trained neural networks, more efficient neural networks can further designed. For impurity models, we reduce the complexity of the conventional Hirsch-Fye algorithm and accelerate the simulation significantly. By deeply integrating the advanced machine learning techniques, SLMC can be expected to play a more important role in exploring the many-body physics.