Principal component analysis for fractional quantum Hall states in bilayer systems

Hengxi Ji, Na Jiang, Xin Wan

Yangdong Zheng, Anju Sawada, Z. F. Ezawa

Zhang, Zhe, Jiajie Qiao, Xiaoliang Wu +2 more

For the special single-layer fractional quantum Hall system with a filling factor of 5/2, which has an even denominator, this paper uses principal component analysis (PCA) to study its behavior under the breaking of particle-hole symmetry. By introducing a model three-body potential to represent the mechanism of particle-hole symmetry breaking, the paper finds that the 5/2 system evolves into two types of special topological quantum states with non-Abelian statistics as the strength and direction of the three-body potential vary. The transition points of these states correspond to the particle-hole symmetric pure Coulomb interaction system. Our results validate the applicability of machine learning as a new research tool in fractional quantum Hall systems. Furthermore, machine learning directly analyzes the raw wave functions, without relying on prior empirical theoretical assumptions and models, making it applicable to a broader range of fractional quantum Hall systems experiencing phase transitions due to particle-hole symmetry breaking.

Layla Hormozi

Zhe Zhang, Jiajie Qiao, Baobing Zheng +1 more

= 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 (PH) symmetry breaking. By introducing a model three-body potential to represent the mechanism of PH 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.

Na Jiang, Min Lu

We study the behavior of two-dimensional electron gas in the fractional quantum Hall (FQH) regime in the presence of disorder potential. The principal component analysis is applied to a set of disordered Laughlin ground state model wave function to enable us to distill the model wave function of the pure Laughlin state. With increasing the disorder strength, the ground state wave function is expected to deviate from the Laughlin state and eventually leave the FQH phase. We investigate the phase transition from the Laughlin state to a topologically trivial state by analyzing the overlap between the random sample wave functions and the distilled ground state wave function. It is proposed that the cross point of the principal component amplitude and its counterpart is the critical disorder strength, which marks the collapse of the FQH regime.