Quantum Hall Effect on the Flag Manifold F_2

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.Comment: 23 pages, two sections and references added, misprints corrected, version to appear in IJMP

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy

Periodic Structures with Rashba Interaction in Magnetic Field

We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U(x) and the Rashba interaction of coupling constant k_{so}. By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k_{so} and U(x)=0, we analyze again the system by deriving different results. Considering the strong $B$ case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point \lambda_{k,\sigma}=\pm\sq{1\over 2}, we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B=0 and U(x) is arbitrary.Comment: 24 pages, references added, misprints corrected. Version to appear in JP

A Matrix Model for Bilayered Quantum Hall Systems

We develop a matrix model to describe bilayered quantum Hall fluids for a series of filling factors. Considering two coupling layers, and starting from a corresponding action, we construct its vacuum configuration at \nu=q_iK_{ij}^{-1}q_j, where K_{ij} is a 2\times 2 matrix and q_i is a vector. Our model allows us to reproduce several well-known wave functions. We show that the wave function \Psi_{(m,m,n)} constructed years ago by Yoshioka, MacDonald and Girvin for the fractional quantum Hall effect at filling factor {2\over m+n} and in particular \Psi_{(3,3,1)} at filling {1\over 2} can be obtained from our vacuum configuration. The unpolarized Halperin wave function and especially that for the fractional quantum Hall state at filling factor {2\over 5} can also be recovered from our approach. Generalization to more than 2 layers is straightforward.Comment: 14 pages, minor changes in introduction and references added, published in JP