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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:su-118807 |
| Date | January 2015 |
| Creators | Majidzadeh Garjani, Babak |
| Publisher | Stockholms universitet, Fysikum, Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita), Stockholm |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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