Normalizing Flows for Multimodal and Extended-Mode Lattice Field Theories*

Probability distributions are ubiquitous in physics and form the basis for our descriptions of quantum and statistical systems. For example, the field of lattice quantum field theory examines physical theories in the strong coupling regime where perturbative methods cannot be applied, conventionally requiring calculations that involve numerically intensive Monte Carlo sampling of field configurations. Normalizing flows have emerged as a promising class of generative machine learning models that learn and exactly sample from complicated target distributions. Here, we discuss the application of normalizing flows as samplers for lattice quantum field theories. In example applications to toy lattice field theories, we incorporate physical constraints such as symmetry into the flow architecture, overcoming the issue of partial mode structure undersampling often seen in normalizing flows applied to theories with spontaneous symmetry breaking. The resulting generative models are shown to capture the full mode structure of the target distribution.