Machine learning topological phases in real space

We develop a supervised machine learning algorithm that is able to learn topological phases for finite systems in real space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector-ensembling procedure. We employ our algorithm to successfully recover topological phase diagrams of Su-Schrieffer-Heeger models from data in real space using decision trees and show how entropy-based criteria can be used to retrieve a topological signal detailing how topological information is distributed along the lattice. Our results demonstrate that learning topological phases in real space may be a viable alternative to wavevector space computations, especially in cases when computing topological invariants in wavevector space is impossible or infeasible (e.g. in disordered systems).