Self-reasoning assisted learning for non-Abelian gauge fields design

Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behavior of anyons, in which the input and outcome of non-Abelian braiding are connected by a unitary matrix. Implementing braiding in a classical system can assist the experimental investigation of non-Abelian physics. However, the design of non-Abelian gauge fields faces numerous challenges stemming from the intricate interplay of group structures, Lie algebra properties, representation theory, topology, and symmetry breaking. The extreme diversity makes it a powerful tool for the study of condensed matter physics. Whereas the widely used artificial intelligence with data-driven approaches has greatly promoted the development of physics, most works are limited on the data-to-data design. Here we propose a self-reasoning assistant learning framework capable of directly generating non-Abelian gauge fields. This framework utilizes the forward diffusion process to capture and reproduce the complex patterns and details inherent in the target distribution through continuous transformation. Then the reverse diffusion process is used to make the generated data closer to the distribution of the original situation. Thus, it owns strong self-reasoning capabilities, allowing us to automatically discover the feature representation and capture more subtle relationships from the data set. Moreover, the self-reasoning eliminates the need for manual feature engineering and simplifies the process of model building. Our framework offers a disruptive paradigm shift to parse complex physical processes, automatically uncovering patterns from massive data sets.