240 research outputs found
Chiral Spin Liquids and Quantum Error Correcting Codes
The possibility of using the two-fold topological degeneracy of spin-1/2
chiral spin liquid states on the torus to construct quantum error correcting
codes is investigated. It is shown that codes constructed using these states on
finite periodic lattices do not meet the necessary and sufficient conditions
for correcting even a single qubit error with perfect fidelity. However, for
large enough lattice sizes these conditions are approximately satisfied, and
the resulting codes may therefore be viewed as approximate quantum error
correcting codes.Comment: 9 pages, 3 figure
Understanding the dynamics of fractional edge states with composite fermions
Fractional edge states can be viewed as integer edge states of composite
fermions. We exploit this to discuss the conductance of the fractional
quantized Hall states and the velocity of edge magnetoplasmons.Comment: 3 pages, revte
Spin and orbital effects in a 2D electron gas in a random magnetic field
Using the method of superbosonization we consider a model of a random
magnetic field (RMF) acting on both orbital motion and spin of electrons in two
dimensions. The method is based on exact integration over one particle degrees
of freedom and reduction of the problem to a functional integral over
supermatrices . We consider a general case when
both the direction of the RMF and the g-factor of the Zeeman splitting are
arbitrary. Integrating out fast variations of we come to a standard
collisional unitary non-linear -model. The collision term consists of
orbital, spin and effective spin-orbital parts. For a particular problem of a
fixed direction of RMF, we show that additional soft excitations identified
with spin modes should appear. Considering % -correlated weak RMF and
putting g=2 we find the transport time . This time is 2 times
smaller than that for spinless particles.Comment: 9 pages, no figure
Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice
The Hofstadter problem is studied on hexagonal lattice. We first establish a
relation between the spectra for the hexagonal lattice and for its dual he
triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain
the Bethe-ansatz equations for this system.Comment: 8 pages, latex, revised version for Phys. Lett.
Energy-level statistics and localization of 2d electrons in random magnetic fields
Using the method of energy-level statistics, the localization properties of
electrons moving in two dimensions in the presence of a perpendicular random
magnetic field and additional random disorder potentials are investigated. For
this model, extended states have recently been proposed to exist in the middle
of the band. In contrast, from our calculations of the large- behavior of
the nearest neighbor level spacing distribution and from a finite size
scaling analysis we find only localized states in the suggested energy and
disorder range.Comment: 4 pages LaTeX, 4 eps-figures. to appear in Physica
Magnetoresistance of composite fermions at \nu=1/2
We have studied temperature dependence of both diagonal and Hall resistivity
in the vicinity of . Magnetoresistance was found to be positive and
almost independent of temperature: temperature enters resistivity as a
logarithmic correction. At the same time, no measurable corrections to the Hall
resistivity has been found. Neither of these results can be explained within
the mean-field theory of composite fermions by an analogy with conventional
low-field interaction theory. There is an indication that interactions of
composite fermions with fluctuations of the gauge field may reconcile the
theory and experiment.Comment: 9 pages, 4 figure
Electron Localization in a 2D System with Random Magnetic Flux
Using a finite-size scaling method, we calculate the localization properties
of a disordered two-dimensional electron system in the presence of a random
magnetic field. Below a critical energy all states are localized and the
localization length diverges when the Fermi energy approaches the
critical energy, {\it i.e.} . We find that
shifts with the strength of the disorder and the amplitude of the random
magnetic field while the critical exponent () remains unchanged
indicating universality in this system. Implications on the experiment in
half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request),
#phd1
Superconductors with Topological Order
We propose a mechanism of superconductivity in which the order of the ground
state does not arise from the usual Landau mechanism of spontaneous symmetry
breaking but is rather of topological origin. The low-energy effective theory
is formulated in terms of emerging gauge fields rather than a local order
parameter and the ground state is degenerate on topologically non-trivial
manifolds. The simplest example of this mechanism of superconductivty is
concretely realized as global superconductivty in Josephson junction arrays.Comment: 4 pages, no figure
Magnetoresistance of Two-Dimensional Fermions in a Random Magnetic Field
We perform a semiclassical calculation of the magnetoresistance of spinless
two-dimensional fermions in a long-range correlated random magnetic field. In
the regime relevant for the problem of the half filled Landau level the
perturbative Born approximation fails and we develop a new method of solving
the Boltzmann equation beyond the relaxation time approximation. In absence of
interactions, electron density modulations, in-plane fields, and Fermi surface
anisotropy we obtain a quadratic negative magnetoresistance in the weak field
limit.Comment: 12 pages, Latex, no figures, Nordita repor
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