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On the Rank of the Reduced Density Operator for the Laughlin State and Symmetric Polynomials
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

One effective tool to probe a system revealing topological order is to biparti- tion the system in some way and look at the properties of the reduced density operator corresponding to one part of the system. In this thesis we focus on a bipartition scheme known as the particle cut in which the particles in the system are divided into two groups and we look at the rank of the re- duced density operator. In the context of fractional quantum Hall physics it is conjectured that the rank of the reduced density operator for a model Hamiltonian describing the system is equal to the number of quasi-hole states. Here we consider the Laughlin wave function as the model state for the system and try to put this conjecture on a firmer ground by trying to determine the rank of the reduced density operator and calculating the number of quasi-hole states. This is done by relating this conjecture to the mathematical properties of symmetric polynomials and proving a theorem that enables us to find the lowest total degree of symmetric polynomials that vanish under some specific transformation referred to as clustering transformation. 

Place, publisher, year, edition, pages
Stockholm: Stockholm University, 2015. , 107 p.
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
URN: urn:nbn:se:su:diva-118807OAI: diva2:839574
2015-05-29, Stockholm, 13:00 (English)
Available from: 2016-05-03 Created: 2015-07-03 Last updated: 2016-05-03Bibliographically approved

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Department of PhysicsNordic Institute for Theoretical Physics (Nordita)
Condensed Matter Physics

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