Constructing the quantum Hall system on the Grassmannians Gr2(CN)

30th International Colloquium on Group Theoretical Methods in Physics

Ball, F.^1 ; Behtash, A.^1 ; Kurkuolu, S.^1 ; Unal, G.^1

Department of Physics, Middle East Technical University, Dumlupinar Boulevard, Cankaya, Ankara

06800, Turkey^1

关键词: Explicit constructions;    Incompressible fluid;    Magnetic monopoles;    Plucker coordinates;    Quantum Hall systems;    Theoretical technique;    Two point correlation functions;    Wigner d-functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012015/pdf
DOI  :  10.1088/1742-6596/597/1/012015

来源: IOP

【 摘 要 】

In this talk, we give the formulation of Quantum Hall Effects (QHEs) on the complex Grassmann manifolds Gr2(CN). We set up the Landau problem in Gr2(CN), solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the SU(N) Wigner D-functions for charged particles on Gr2(CN) under the influence of abelian and non-abelian background magnetic monopoles or a combination of these thereof. For the simplest case of Gr2(C4) we provide explicit constructions of the single and many- particle wavefunctions by introducing the Plucker coordinates and show by calculating the two-point correlation function that the lowest Landau level (LLL) at filling factor v = 1 forms an incompressible fluid. Finally, we heuristically identify a relation between the U(1) Hall effect on Gr2(C4) and the Hall effect on the odd sphere S5, which is yet to be investigated in detail, by appealing to the already known analogous relations between the Hall effects on CP3and CP7and those on the spheres S4and S8, respectively. The talk is given by S. Kurkuolu at the Group 30 meeting at Ghent University, Ghent, Belgium in July 2014 and based on the article by F.Ball, A.Behtash, S. Kurkuolu, G.Unal [1].