Principal component analysis for 5/2 fractional quantum Hall states
Abstract
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.
Cite
@article{arxiv.2503.04029,
title = {Principal component analysis for 5/2 fractional quantum Hall states},
author = {Zhe Zhang and Jiajie Qiao and Xiaoliang Wu and Shaowen Yu and Qin Jin},
journal= {arXiv preprint arXiv:2503.04029},
year = {2025}
}