Machine learning study for disorder effect at a half-filled high Landau level

Abstract

The robustness against disorder scattering is crucial for experimentally observing the predicted charge density waves (CDWs) in a fractional quantum Hall (FQH) system with partially-filled topmost Landau level (LL). Here, we applied two types of machine learning (ML) methods to study the influence of the disorder on an example system with half-filled N = 2 LL. Through the unsupervised principal component analysis (PCA) method, we recognize that a CDW stripe phase is represented by two principal components, which alternatively dominate in weak scattering case and coherently collapse at strong scattering. A combination of these two PCA components enables us to fully describe the evolution of the stripe phase and to determine its critical transition point towards a random disorder phase. A practice with the supervised neural network (NN) method also provides us with the numerically same boundary for the two separated phases. These ML approaches have proved to be effective tools for our system as their results are well compatible with previous numerical works. Moreover, the nonnecessity to the explicit knowledge of the states extends their potential to study other unfamiliar disordered systems.