Modeling Many-Body Physics with Restricted Boltzmann Machines

Neural networks hold the potential to significantly improve the efficiency of various simulation strategies in condensed matter and statistical physics. Foremost is the idea of generative modeling, or sampling an approximate probability distribution or wavefunction, using stochastic neural networks. In this talk, we survey the uses of one such neural network called a Restricted Boltzmann Machine (RBM) in the field of many-body physics. We illustrate the ability of RBMs to "learn" by being trained with data from finite-size lattice Hamiltonians, and ask whether the resulting model is an efficient and faithful representation of the original system. We explore various quantum and classical examples, including systems with conventional phases and phase transitions, as well as unconventional and topological order. Finally, we discuss the potential for RBMs to augment traditional Monte Carlo approaches, examine their representational efficiency for compressing quantum wavefunctions, and discuss connections to Tensor Networks and related numerical methods.