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Strongly Correlated Systems Under High Magnetic Field: A Mixed Landau Levels Description for Fractional Quantum Hall Effect
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Strongly Correlated Systems Under High Magnetic Field: A Mixed Landau Levels Description for Fractional Quantum Hall Effect. |
| 개인저자 | Bandyopadhyay, Sumanta. |
| 단체저자명 | Washington University in St. Louis. Physics. |
| 발행사항 | [S.l.]: Washington University in St. Louis., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 211 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781085668460 |
| 학위논문주기 | Thesis (Ph.D.)--Washington University in St. Louis, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Seidel, Alexander. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | Strong correlation among electrons under high magnetic field gives rise to an entirely new arena of emergent physics, namely fractional quantum Hall effect. Such systems have entirely different elementary degrees of freedom and generally, demand non-perturbative approaches to develop a better understanding. In the literature, there are several analytical methodologies and numerical toolkits available to study such a system. Clustering of zeros, parent Hamiltonian, off-diagonal order parameter, parton construction, matrix product states are to be named among a few of those popular methodologies in the existing literature. Most of these methods work well in the lowest Landau level or holomorphic wavefunction framework. It is, however, imperative to develop such methodology to study systems with Landau levels mixing to study more exotic as well as experimentally relevant states. In this work, we have developed particular methodologies, which denounce the traditional importance of the analytic properties of first quantized model wavefunction thereby extend the existing parent Hamiltonian, topological order-parameter, matrix product states descriptions to mixed Landau level systems. Such extension produces a deeper, compact and holistic understanding of universal physics of exotic phases in strongly correlated systems from the microscopic viewpoint, as well as produces interesting new results. Our second quantized/ non-analytic approach allows us to construct the ``entangled Pauli principle", a guidebook to extract universal/topological properties such as braiding statistics, fractional charge quantization, topological degeneracy of the ground states starting from a relatively simple many-body wavefunction, ``root pattern" of fractional quantum Hall state. Such an entangled Pauli principle can be derived from a microscopic parent Hamiltonian setting, thereby provide us a potential tool to probe the non-universal physics in quantum Hall fluids as well. Essentially, entangled Pauli principle is the ``DNA" of fractional quantum Hall states. Using this guiding principle, we have shown ground states with non-abelian excitations, such as Majorana fermion or Fibonacci fermion can be stabilized for two-particle interaction. Fibonacci fermion supports universal quantum gates, thereby a potential candidate for the topologically protected universal quantum computer. Entangled Pauli principle, along with a recently developed topological order parameter for composite fermions, gives rise to Parent Hamiltonian description for composite fermions as well. |
| 일반주제명 | Condensed matter physics. Physics. Nanotechnology. Particle physics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
