64 research outputs found
Coordinate Representation of the One-Spinon One-Holon Wavefunction and Spinon-Holon Interaction
By deriving and studying the coordinate representation for the one-spinon
one-holon wavefunction we show that spinons and holons in the supersymmetric model with interaction attract each other. The interaction causes
a probability enhancement in the one-spinon one-holon wavefunction at short
separation between the particles. We express the hole spectral function for a
finite lattice in terms of the probability enhancement, given by the one-spinon
one-holon wavefunction at zero separation. In the thermodynamic limit, the
spinon-holon attraction turns into the square-root divergence in the hole
spectral function.Comment: 20 pages, 3 .eps figure
From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect
We investigate the algebraic structure of flat energy bands a partial filling
of which may give rise to a fractional quantum anomalous Hall effect (or a
fractional Chern insulator) and a fractional quantum spin Hall effect. Both
effects arise in the case of a sufficiently flat energy band as well as a
roughly flat and homogeneous Berry curvature, such that the global Chern
number, which is a topological invariant, may be associated with a local
non-commutative geometry. This geometry is similar to the more familiar
situation of the fractional quantum Hall effect in two-dimensional electron
systems in a strong magnetic field.Comment: 8 pages, 3 figure; published version with labels in Figs. 2 and 3
correcte
Nonabelian gauge field and dual description of fuzzy sphere
In matrix models, higher dimensional D-branes are obtained by imposing a
noncommutative relation to coordinates of lower dimensional D-branes. On the
other hand, a dual description of this noncommutative space is provided by
higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a
configuration of lower dimensional D-branes in a constant R-R field strength
background. In this paper, we consider a dual description of higher dimensional
fuzzy spheres by introducing nonabelian gauge fields on higher dimensional
spherical D-branes. By using the Born-Infeld action, we show that a fuzzy
-sphere and spherical D-branes with a nonabelian gauge field whose
Chern character is nontrivial are the same objects when is large. We
discuss a relationship between the noncommutative geometry and nonabelian gauge
fields. Nonabelian gauge fields are represented by noncommutative matrices
including the coordinate dependence. A similarity to the quantum Hall system is
also studied.Comment: 28 page
Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
The two-dimensional one-component plasma (2dOCP) is a system of mobile
particles of the same charge on a surface with a neutralising background.
The Boltzmann factor of the 2dOCP at temperature can be expressed as a
Vandermonde determinant to the power . Recent advances in
the theory of symmetric and anti-symmetric Jack polymonials provide an
efficient way to expand this power of the Vandermonde in their monomial basis,
allowing the computation of several thermodynamic and structural properties of
the 2dOCP for values up to 14 and equal to 4, 6 and 8. In this
work, we explore two applications of this formalism to study the moments of the
pair correlation function of the 2dOCP on a sphere, and the distribution of
radial linear statistics of the 2dOCP in the plane
Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
By deriving and studying the coordinate representation for the two-spinon
wavefunction, we show that spinon excitations in the Haldane-Shastry model
interact. The interaction is given by a short-range attraction and causes a
resonant enhancement in the two-spinon wavefunction at short separations
between the spinons. We express the spin susceptibility for a finite lattice in
terms of the resonant enhancement, given by the two-spinon wavefunction at zero
separation. In the thermodynamic limit, the spinon attraction turns into the
square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure
Spin-Hall effect with quantum group symmetry
We construct a model of spin-Hall effect on a noncommutative 4 sphere with
isospin degrees of freedom (coming from a noncommutative instanton) and
invariance under a quantum orthogonal group. The corresponding representation
theory allows to explicitly diagonalize the Hamiltonian and construct the
ground state; there are both integer and fractional excitations. Similar models
exist on higher dimensional noncommutative spheres and noncommutative
projective spaces.Comment: v2: 14 pages, latex. Several changes and additional material; two
extra sections added. To appear in LMP. Dedicated to Rafael Sorkin with
friendship and respec
Quantum Mechanics Model on K\"ahler conifold
We propose an exactly-solvable model of the quantum oscillator on the class
of K\"ahler spaces (with conic singularities), connected with two-dimensional
complex projective spaces. Its energy spectrum is nondegenerate in the orbital
quantum number, when the space has non-constant curvature. We reduce the model
to a three-dimensional system interacting with the Dirac monopole. Owing to
noncommutativity of the reduction and quantization procedures, the Hamiltonian
of the reduced system gets non-trivial quantum corrections. We transform the
reduced system into a MIC-Kepler-like one and find that quantum corrections
arise only in its energy and coupling constant. We present the exact spectrum
of the generalized MIC-Kepler system. The one-(complex) dimensional analog of
the suggested model is formulated on the Riemann surface over the complex
projective plane and could be interpreted as a system with fractional spin.Comment: 5 pages, RevTeX format, some misprints heve been correcte
Electronic Structure of a Hydrogenic Acceptor Impurity in Semiconductor Nano-structures
The electronic structure and binding energy of a hydrogenic acceptor impurity in 2, 1, and 0-dimensional semiconductor nano-structures (i.e. quantum well (QW), quantum well wire (QWW), and quantum dot (QD)) are studied in the framework of effective-mass envelope-function theory. The results show that (1) the energy levels monotonically decrease as the quantum confinement sizes increase; (2) the impurity energy levels decrease more slowly for QWWs and QDs as their sizes increase than for QWs; (3) the changes of the acceptor binding energies are very complex as the quantum confinement size increases; (4) the binding energies monotonically decrease as the acceptor moves away from the nano-structuresâ center; (5) as the symmetry decreases, the degeneracy is lifted, and the first binding energy level in the QD splits into two branches. Our calculated results are useful for the application of semiconductor nano-structures in electronic and photoelectric devices
Super D-Helix
We study `Myers effect' for a bunch of -branes with superstrings
moving in one direction along the branes. We show that the `blown-up'
configuration is the helical -brane, which is self-supported from collapse
by the axial momentum flow. The tilting angle of the helix is determined by the
number of -branes. The radius of the helix is stabilized to a certain value
depending on the number of -branes and the momentum carried by
superstrings. This is actually T-dual version of the supertube recently found
as the `blown-up' configuration of a bunch of superstrings carrying
-brane charge. It is found that the helical configuration preserves
one quarter of the supersymmetry of vacuum.Comment: 13 pages using REVTeX macro, V.3: added references, corrected typos
in the Killing spinor relations, and added discussions on D1/D
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