Research On The Phase Transition Of Fractional Quantum Hall System Based On Machine Learning Method

Fractional quantum Hall effect(FQHE)is one of the most important discoveries in modern condensed matter physics.As a many-body interacting system completely dominated by the interaction between particles,novel topological quantum states are constantly emerging in fractional quantum Hall system.Currently,the understanding of these quantum phase states is not thorough,and mainly relying on some specific phenomenological theories or model wave functions.On the other hand,machine learning,as an important branch of artificial intelligence,has been widely applied in condensed matter physics in recent years.However,most of these applications focus on the special lattice model systems,and there are very few researches on fractional quantum Hall system.In this thesis,different methods of machine learning are used to systematically study the quantum states caused by multiple effects in fractional quantum Hall system and the phase transitions between them.The main work includes the following three parts:Firstly,we initiate an unsupervised machine learning study with the principal component analysis(PCA)for multiple example bilayer fractional quantum Hall systems at fractional filling factors.The results show that the bilayer system exhibit different quantum phase states at different physical limits of the parameter space constructed by the interlayer tunneling effect and the interlayer coupling effect.In addition,some common features in principal component analysis are exploited to recognize the transition and boundary between two competing ground state phases even without a complete softening in the spectrum.We also provide the numerical evidence to confirm a bilayer system as an analogy to its single-layer counterpart at large interlayer tunneling limit.The general approaches with principal component analysis have been applied to determine the collapsing boundaries for phases at the strongly-correlated bilayer limit,the decoupled bilayer limit,and the strong interlayer tunneling limit.Secondly,the robustness of strip-shaped charge density wave states against impurity scattering is researched for a quantum Hall system with half-filled high Landau levels by using principal component analysis and neural network(NN)methods in machine learning,respectively.Through the unsup ervised principal component analysis method,we recognize that the main characteristics of stripe phase can still be represented by several principal components in the wave function,even in the presence of finite intensity disorder scattering.The coheren t collapse of the associated components with scattering intensity marks the transition of the system from a long-range ordered state to a disorder state.Furthermore,we determine the critical impurity scattering intensity of the phase transition by applying principal component analysis and neural network methods,respectively.This research is expected to provide a parametric basis for the subsequent experimental observation of the strip phase state in a real physical system.Finally,principal component analysis is used to investigate the behavior of a special single-layer fractional quantum Hall system with an even denominator for filling factor 5/2 when the particle-hole symmetry is broken.By introducing a model three-body potential to characterize the mechanism of particle-hole breaking,we find that the 5/2 system evolves to two class of special topological quantum states with non-Abelian statistics as the strength and direction of the three-body potential change.Their transition points correspond to the pure Coulomb interaction system with particle-hole symmetry.Since these two types of special states in 5/2system are expected to be used to design qubits in the future,our results reveal that particle-hole breaking will be critical for their existence.The above research results obtained by machine learning method are consistent with some earlier results obtained by traditional numerical calculation,which verifies the applicability of machine learning as a new research method in fractional quantum Hall system.Furthermore,machine learning directly analyzes the original wave function without relying on prior empirical theoretical assumptions and models,hence it can be extended more generally to unfamiliar systems that people have not yet understood.