Self-Reasoning Assistant Learning for non-Abelian Gauge Fields Design

Non-Abelian braiding has attracted substantial attention because of its pivotal role in describing the exchange behaviour 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 stemmed 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 to automatically discover the feature representation and capture more subtle relationships from the dataset. 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 datasets.

Deep learning for the design of non-Hermitian topolectrical circuits

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we introduce several algorithms with multi-layer perceptron (MLP), and convolutional neural network (CNN) in the field of deep learning, to predict the winding of eigenvalues non-Hermitian Hamiltonians. Subsequently, we use the smallest module of the periodic circuit as one unit to construct high-dimensional circuit data features. Further, we use the Dense Convolutional Network (DenseNet), a type of convolutional neural network that utilizes dense connections between layers to design a non-Hermitian topolectrical Chern circuit, as the DenseNet algorithm is more suitable for processing high-dimensional data. Our results demonstrate the effectiveness of the deep learning network in capturing the global topological characteristics of a non-Hermitian system based on training data.