Unsupervised learning of topological phase diagram using topological data analysis

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also data science. Here, we propose the use of topological analysis unsupervised phase diagrams. This is possible because quantum distance can capture shape space formed by Bloch wavefunctions as sweep over Brillouin zone. Therefore, if minimize volume wavefunction through a continuous deformation, will end up forming distinct spaces which depend on topology wavefunctions. Combining this observation with analysis, provides tools such persistence diagram to wavefunctions, cluster together Hamiltonians that give rise similar diagrams after deformation. By examining these clusters well representative clusters, draw distinguish between topologically trivial nontrivial phases. Our proposal be interpreted finding geodesics 1D zone, minimal surfaces 2D higher-dimensional zones. Using interpretation, guarantee convergence minimization under certain conditions, an outstanding feature our algorithm. We demonstrate working principles algorithm using various models.