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Geometric Aspects in the Hamiltonian Theory of the Fractional Quantum Hall Effect

Abstract : The topological properties in quantum Hall systems are thoroughly studied in the past thirty years. In constrast, the geometric aspects of quantum Hall systems are far from being fully understood. In this thesis, I am going to investigate the geometric aspects from the view of the composite fermion Hamiltonian theory and test the response of quantum Hall states under anisotropic perturbation. I find in the presence of anisotropy, composite fermions receive mixing effects between different composite fermion Landau levels. A variational metric can be combined to the composite fermions in order to minimize such an effect. The activation gaps and neutral collective gaps are calculated for a quantum Hall system with tilted magnetic field. The former exhibits a robustness while the latter is susceptible to anisotropic perturbation. The charge density wave states under mass anisotropy are also studied. The bubble phase is found to be strongly suppressed by the mass anisotropy. All the first-order phase transitions present in the isotropic case are replaced by continuous phase transitions in the anisotropic case.
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Submitted on : Wednesday, February 17, 2021 - 2:35:10 PM
Last modification on : Friday, February 19, 2021 - 3:27:28 AM


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  • HAL Id : tel-03144255, version 1


Kang Yang. Geometric Aspects in the Hamiltonian Theory of the Fractional Quantum Hall Effect. Physics [physics]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS425⟩. ⟨tel-03144255⟩



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