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 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 a different lattice from the training data, which implies the universal feature of the flat-band states constructed by the molecular-orbital representation.