On the Rank of the Reduced Density Operator for the Laughlin State and Symmetric Polynomials
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
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.
Condensed Matter Physics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-118807OAI: oai:DiVA.org:su-118807DiVA: diva2:839574
2015-05-29, Stockholm, 13:00 (English)
Fuchs, Jürgen, Professor