Phase transition extracted by principal component analysis in the disordered Moore–Read state

We study the influence of disorder on the Moore–Read state by principal component analysis (PCA), which is one of the ground state candidates for the 5/2 fractional Hall state. By using PCA, the topological features of the ground state wave functions with different disorder strengths can be distilled. As the disorder strength increases, the Moore–Read state will be destroyed. We explore the phase transition by analyzing the overlaps between the random sample wave functions and the topologically distilled state. The cross-point between the amplitudes of the principal component and its counterpart is the phase transition point. Additionally, the origin of the second component comes from the excited states, which is different from the Laughlin state.