Quantum Hall Effect on the Flag Manifold F_2

Details Quantum Hall Effect on the Flag Manifold F_2 Quantum Hall Effect on the Flag Manifold F_2

2006-10-13

arxiv.org/abs/hep-th/0610157v2

Int.J.Mod.Phys.A23:3129-3154,2008

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, two sections and references added, misprints corrected, version to appear in IJMPA

Scientific paper

10.1142/S0217751X08040524

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $\nu =1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.

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