Principal component analysis of quantum Hall wave functions

The fractional quantum Hall effect demonstrates the robustness of topological properties in many-body systems. The effect of mass and interaction anisotropy can be understood in terms of a geometrical description. We present a study of the evolution of quantum Hall wave functions with interaction anisotropy by a statistical learning technique known as the principal component analysis (PCA). We show that the topological and geometrical aspects of a family of wave functions can be readily separated by the PCA. We discuss how to use the PCA to extract wave function metric and to determine the stability of a fractional quantum Hall phase.