Machine learning topological phases in real space

We develop a supervised machine learning algorithm that is able to learn topological phases for finite condensed matter systems in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector-ensembling procedure. We combine our algorithm with decision trees to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from lattice data in real space and show how the Gini impurity of ensembles of lattice eigenvectors can be used to retrieve a topological signal detailing how topological information is distributed along the lattice. The discovery of local Gini topological signals from the analysis of data from several thousand SSH systems illustrates how machine learning can advance the research and discovery of new quantum materials with exotic properties that may power future technological applications such as quantum computing.