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Kitaev models for topologically ordered phases of matter
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Kitaev modeller för topologisk ordnade faser av materia (Swedish)
Abstract [en]

Condensed matter physics is the study of the macroscopic and microscopic properties of condensed phases of matter. For quite some time, Landau’s symmetry breaking theory was believed to describe and explain the nature of any phase transition. However, since the late 1980s, it has become apparent that it is necessary to introduce some new kind of order, named topological order, that transcends the traditional symmetry description. In this thesis we will study the Kitaev model, which is a Hamiltonian lattice model that allows one to incorporate the concept of topological order, as well as the corresponding operators and algebras. First, we consider the model on an infinite lattice, and show how to relate local and global degrees of freedom of the anyons/quasi-particles living on sites to the ribbon operators. Afterwards, we introduce holes and an external boundary to the lattice, and examine the ramifications of this generalization in terms of the ground state degeneracy. Lastly, we verify that the algebra formed by boundary site operators has the structure of a quasi-Hopf algebra. 

Place, publisher, year, edition, pages
2017. , p. 46
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kau:diva-62814OAI: oai:DiVA.org:kau-62814DiVA, id: diva2:1136214
Subject / course
Physics
Educational program
Bachelor Programme in Physics , 180 hp
Presentation
2017-06-12, 21D304, 10:15 (English)
Supervisors
Examiners
Available from: 2017-12-21 Created: 2017-08-25 Last updated: 2017-12-21Bibliographically approved

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fulltext(937 kB)54 downloads
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Type fulltextMimetype application/pdf

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Condensed Matter Physics

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CiteExportLink to record
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