Multifaceted machine learning of competing orders in disordered interacting systems

While the nonperturbative interaction effects in the fractional quantum Hall regime can be readily simulated through exact diagonalization, it has been challenging to establish a suitable diagnostic that can label different phases in the presence of competing interactions and disorder. Here we introduce a multifaceted framework using a simple artificial neural network (ANN) to detect defining features of a fractional quantum Hall state, a charge-density-wave state and a localized state using the entanglement spectra and charge density as independent input. We consider the competing effects of a perturbing interaction (l=1 pseudopotential ΔV1), a disorder potential W, and the Coulomb interaction to the system at filling fraction ν=1/3. Our phase diagram benchmarks well against previous estimates of the phase boundary along the axes of our phase diagram where other measures exist. Moreover, exploring the entire two-dimensional phase diagram, we establish the robustness of the fractional quantum Hall state and map out the charge-density-wave microemulsion phase wherein droplets of the charge-density-wave region appear before the charge density wave is completely disordered. Hence we establish that the ANN can access and learn the defining traits of topological as well as broken symmetry phases using multifaceted inputs of entanglement spectra and charge density.