Persistent Homology Analysis of Phase Transitions in Quantum Systems

Explore the application of topological machine learning techniques to understand complex physical systems in this 43-minute lecture by Daniel Leykam from PCS Institute for Basic Science. Delve into the concept of persistent homology, a method designed to extract relevant information from sparse data by computing topological features across various scales. Learn how this technique identifies meaningful features in point cloud data by distinguishing persistent patterns from less robust ones. Discover recent applications of persistent homology in condensed matter physics, including the detection of phase transitions in classical and quantum spin models. Gain insights into the identification of order-disorder transitions in a generalized Aubry-Andre-Harper model. Understand the advantages of persistent homology over traditional deep learning methods, particularly when dealing with limited datasets in the study of topological and correlated quantum phases of matter.