2024/01/31 by Yang Long, Haoran Xue, Long, Yang +3 · 1 citation
Computer Science · #Chaos-based Image/Signal Encryption #Data Analysis #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Neural Networks and Applications #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2401.17968
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies have revealed the intriguing topology of complex-energy, or non-Hermitian bands. For example, the spectral winding of complex-energy bands can from unique topological structures like braids, holding promise for advancing quantum computing. However, discussions of complex-energy braids have been largely limited to the Abelian braid group \mathbbB2 for its relative simplicity, while identifying topological non-Abelian braiding is still difficult since it has no universal topological invariant for characterization. Here, we present a machine learning algorithm for the unsupervised identification of non-Abelian braiding of multiple complex-energy bands. The consistency with Artin's well-known topological equivalence conditions in braiding is demonstrated. Inspired by the results from unsupervised learning, we also introduce a winding matrix as a topological invariant in charactering the braiding topology and unveiling the bulk-edge correspondence of non-Abelian braided non-Hermitian bands. Finally, we extend our approach to identify non-Abelian braiding topology in 2D/3D exceptional semimetals and successfully address the unknotting problem in an unsupervised manner.