Quantum Hall Effect on the Flag Manifold F_2

Abstract

The Landau problem on the flag manifold ${\mathbf{F}}_2=SU(3)/U(1)\times U(1)$ 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 ${\mathbf{F}}_2$, are the SU(3) Wigner $\mathcal{D}$-functions satisfying two constraints. Using the ${\mathbf{F}}_2$ 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.

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

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• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Riccati Diagonalization of Hermitian Matrices
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• Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations
• Interlayer coherence and entanglement in bilayer quantum Hall states at filling factor $\nu =2/\lambda$
• SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Electromagnetic Excitations of A_n Quantum Hall Droplets