Quantum hall effect on grassmann manifolds

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2014
Ballı, Fatih
In this work we formulate Quantum Hall E ect(QHE) on Grassmann manifolds Gr2(CN). We, rst give a self-contained reviews of integer QHE on R2, S2 CP1 and CP2 which are oriented towards our purposes. Then, we set up the Landau problem on Gr2(CN) and discuss and formulate the wave functions, energy levels, degeneracy, incompressibility and spatial density properties. Group theoretical techniques are used to explore these properties for both abelian and non-abelian backgrounds and the wave functions are expressed in terms of suitably restricted subset of Wigner-D functions. For the simplest case of QHE on Gr2(C4) with pure U(1) gauge elds, we introduce Plücker coordinates and express the wave functions and the gauge elds in these coordinates. We calculate the two-point correlation function and deduce the incompressibility of Quantum Hall liquid on Gr2(C4). We indicate how these formulation in local coordinates may be generalized to all Gr2(CN).

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Citation Formats
F. Ballı, “Quantum hall effect on grassmann manifolds,” M.S. - Master of Science, Middle East Technical University, 2014.