Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness

We study the characteristic probability density distribution of random flat band models by machine learning. The models considered here are constructed on the basis of the molecular-orbital representation, which guarantees the existence of the macroscopically degenerate zero-energy modes even in the presence of randomness. We find that flat band states are successfully distinguished from conventional extended and localized states, indicating the characteristic feature of the flat band states. We also find that the flat band states can be detected when the target data are defined in the different lattice from the training data, which implies the universal feature of the flat band states constructed by the molecular-orbital representation.