Topological properties of diagrammatic perturbation theory for anyon system : focusing on anyon interferometer = 애니온계에 대한 도형적 섭동이론의 위상적 성질 : 애니온 간섭계 중심으로focusing on anyon interferometer

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Perturbation theory is a main tool to understand the effect of complicated interactions in physical system. The perturbative expansion of physical observable in fermionic and bosonic syste can be described by Feynman diagrams. According to the linked cluster theorem, one of the basic rule of the quantum field theory, only the connected diagrams affect to physical observable, and the disconnected diagram cancelled each other. On the other hand, anyons are quasiparticles in two dimensions, not belonging to the bosons and fermions, and obeying fractional statistics. Anyons are classified according to their braiding properties, Abelian anyon or non-Abelian anyon. Due to the braiding properties, it is believed as key element of the topological quantum computation. Despite of a much effort, there is no unequivocal evidence of anyon in experimentally. In this dissertation, we apply the diagrammatic perturbation theory to the anyon system. We find that the anyon braiding results in 'topological connection' which has been never discussed before. We show that a disconnected diagram for bosons and fermions can be topologically connected and contribute to physical observable for anyons. We propose an interferometer setup operating in the fractional quantum Hall system to detect such a `topologically connected diagram' or equivalently fractional statistics.
Advisors
Sim, Heung-Sunresearcher심흥선researcher
Description
한국과학기술원 :물리학과,
Publisher
한국과학기술원
Issue Date
2018
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 물리학과, 2018.2,[vi, 52 p. :]

Keywords

Condensed matter physics▼aAnyon▼aPerturbation theory▼aFeynman diagram▼aFractional quantum Hall system▼aanyon interferometer; 응집 물질 물리▼a애니온▼a섭동 이론▼a파인만 도형▼a분수 양자 홀 효과▼a애니온 간섭계

URI
http://hdl.handle.net/10203/264655
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=734293&flag=dissertation
Appears in Collection
PH-Theses_Ph.D.(박사논문)
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