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 nu = 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. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this study, we employed the principal component analysis (PCA) method to investigate bilayer fractional quantum Hall (FQH) systems considering the interlayer tunneling effect and Coulomb interaction. By utilizing common features in the PCA, we were able to recognize the transitions and boundaries between competing ground state phases, even in the absence of complete spectrum softening. Numerical evidence was provided to confirm the analogy between the bilayer system and its single-layer counterpart under large interlayer tunneling limit. The general approach with PCA was applied to determine the phase boundaries in strongly-correlated bilayer limit, decoupled bilayer limit, and strong interlayer tunneling limit, resulting in qualitatively similar phase diagrams as previous numerical studies without relying on explicit knowledge of the states. Therefore, our PCA study can be extended to other unfamiliar bilayer systems.