9,672 research outputs found
Sharp and Smooth Boundaries of Quantum Hall Liquids
We study the transition between sharp and smooth density distributions at the
edges of Quantum Hall Liquids in the presence of interactions. We find that,
for strong confining potentials, the edge of a liquid is described by
the Fermi Liquid theory, even in the presence of interactions, a
consequence of the chiral nature of the system. When the edge confining
potential is decreased beyond a point, the edge undergoes a reconstruction and
electrons start to deposit a distance magnetic lengths away from the
initial QH Liquid. Within the Hartree-Fock approximation, a new pair of
branches of gapless edge excitations is generated after the transition. We show
that the transition is controlled by the balance between a long-ranged
repulsive Hartree term and a short-ranged attractive exchange term. Such
transition also occurs for Quantum Dots in the Quantum Hall Regime, and should
be observable in resonant tunneling experiments. Electron tunneling into the
reconstructed edge is also discussed.Comment: 28 pages, REVTeX 3.0, 18 figures available upon request,
cond-mat/yymmnn
Non-diagonal solutions of the reflection equation for the trigonometric vertex model
We obtain a class of non-diagonal solutions of the reflection equation for
the trigonometric vertex model. The solutions can be expressed
in terms of intertwinner matrix and its inverse, which intertwine two
trigonometric R-matrices. In addition to a {\it discrete} (positive integer)
parameter , , the solution contains {\it continuous}
boundary parameters.Comment: Latex file, 14 pages; V2, minor typos corrected and a reference adde
Exact solution of the trigonometric vertex model with non-diagonal open boundaries
The trigonometric vertex model with {\it generic
non-diagonal} boundaries is studied. The double-row transfer matrix of the
model is diagonalized by algebraic Bethe ansatz method in terms of the
intertwiner and the corresponding face-vertex relation. The eigenvalues and the
corresponding Bethe ansatz equations are obtained.Comment: Latex file, 25 pages; V2: minor typos corrected, the version appears
in JHE
Coulomb Drag of Edge Excitations in the Chern-Simons Theory of the Fractional Quantum Hall Effect
Long range Coulomb interaction between the edges of a Hall bar changes the
nature of the gapless edge excitations. Instead of independent modes
propagating in opposite directions on each edge as expected for a short range
interaction one finds elementary excitations living simultaneously on both
edges, i.e. composed of correlated density waves propagating in the same
direction on opposite edges. We discuss the microscopic features of this
Coulomb drag of excitations in the fractional quantum Hall regime within the
framework of the bosonic Chern-Simons Landau-Ginzburg theory. The dispersion
law of these novel excitations is non linear and depends on the distance
between the edges as well as on the current that flows through the sample. The
latter dependence indicates a possibility of parametric excitation of these
modes. The bulk distributions of the density and currents of the edge
excitations differ significantly for short and long range interactions.Comment: 11 pages, REVTEX, 2 uuencoded postscript figure
Finite Size Analysis of Luttinger Liquids with a source of 2k_f Scattering
Numerical analysis of the spectrum of large finite size Luttinger liquids
(g<1) in the presence of a single source of 2k_f scattering has been made
possible thanks to an effective integration of high degrees of freedom.
Presence of irrelevant operators and their manifestation in transport are
issues treated independently. We confirm the existence of two irrelevant
operators: particle hopping and charge oscillations, with regions of dominance
separated by g=1/2. Temperature dependence of conductance is shown to be
dominated by hopping alone. Frequency dependence is affected by both irrelevant
operators.Comment: 4 pages, LaTex (RevTex), 3 PostScript figures appende
Gaussian field theories, random Cantor sets and multifractality
The computation of multifractal scaling properties associated with a critical
field theory involves non-local operators and remains an open problem using
conventional techniques of field theory. We propose a new description of
Gaussian field theories in terms of random Cantor sets and show how universal
multifractal scaling exponents can be calculated. We use this approach to
characterize the multifractal critical wave function of Dirac fermions
interacting with a random vector potential in two spatial dimensions. We show
that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace
numerical calculation
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