Principal component analysis for fractional quantum Hall states in bilayer systems

We initiate an unsupervised machine learning (ML) study with the principal component analysis (PCA) for two example bilayer fractional quantum Hall (FQH) systems at filling factors ν=4/5 and 2/3 where the interlayer tunneling effect and Coulomb interaction are considered. Some common features in PCA are exploited to recognize the transition and boundary between two competing ground state (GS) phases even without a complete softening in the spectrum. We also provide the numerical evidence to confirm a bilayer system as an analogy to its single-layer counterpart at large interlayer tunneling limit. The general approaches with PCA have been applied to determine the collapsing boundaries for phases at the strongly-correlated bilayer limit, the decoupled bilayer limit, and the strong interlayer tunneling limit, which lead to the qualitatively similar phase diagrams as previous numerical studies but do not rely on explicit knowledge of the states. Thus, our PCA study is extendable for other unfamiliar bilayer systems.