Unveiling particle-hole symmetry breaking and topological transitions in the v = 5/2 fractional quantum hall state via principal component analysis.

The v = 5/2 fractional quantum Hall (FQH) state, as a special single-layer system with an even-denominator filling factor, serves as a promising platform for exploring exotic topological phases. In this study, we employ principal component analysis (PCA), an unsupervised machine learning technique, to investigate the evolution of many-body wavefunctions under particle-hole symmetry breaking. By introducing a model three-body potential to represent the mechanism of particle-hole symmetry breaking, we demonstrate that the ground state of the system transitions continuously between two distinct non-Abelian topological states, namely the Pfaffian and the anti-Pfaffian, as the strength and direction of the three-body term vary. Notably, the critical transition point corresponds to the pure Coulomb interaction, which preserves PH symmetry. Our results demonstrate that machine learning techniques, exemplified by PCA, provide a powerful and unbiased tool to identify and characterize topological phase transitions in FQH systems. Unlike traditional approaches that rely on predefined model wavefunctions, our method analyzes raw many-body wavefunctions directly, offering a model-independent framework applicable to a broader class of FQH systems undergoing topological transitions driven by symmetry breaking.