33 research outputs found
Spin-pairing instabilities at the coincidence of two Landau levels
The effect of interactions near the coincidence of two Landau levels with
opposite spins at filling factor 1/2 is investigated. By mapping to Composite
Fermions it is shown that the fluctuations of the gauge field induces an
effective attractive Fermion interaction. This can lead to a spin-singlet
ground state that is separated from the excited states by a gap. The magnitude
of the gap is evaluated. The results are consistent with the recently observed
half-polarized states in the FQHE at a fixed filling factor. It is suggested
that similar anomalies exist for other spin configurations in degenerate
spin-up and spin-down Landau levels. An experiment for testing the spin-singlet
state is proposed.Comment: to be published in Physical Review
Coulomb drag as a signature of the paired quantum Hall state
Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, we
study the Coulomb drag in a two-layer system with Landau level filling factor
. We find that the drag conductivity in the incompressible paired
quantum Hall state at zero temperature can be finite. The drag conductivity is
also greatly enhanced above , at which the transition between the weakly
coupled compressible liquids and the paired quantum Hall liquid takes place. We
discuss the implications of our results for the recent experiment.Comment: 4 pages, 1 figure included, replaced by the published versio
Monte Carlo Simulations of Interacting Anyon Chains
A generalized version of the valence-bond Monte Carlo method is used to study
ground state properties of the 1+1 dimensional quantum -state Potts models.
For appropriate values of these models can be used to describe interacting
chains of non-Abelian anyons --- quasiparticle excitations of certain exotic
fractional quantum Hall states.Comment: 4 pages, 5 figure
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
A probabilistic evolutionary optimization approach to compute quasiparticle braids
Topological quantum computing is an alternative framework for avoiding the
quantum decoherence problem in quantum computation. The problem of executing a
gate in this framework can be posed as the problem of braiding quasiparticles.
Because these are not Abelian, the problem can be reduced to finding an optimal
product of braid generators where the optimality is defined in terms of the
gate approximation and the braid's length. In this paper we propose the use of
different variants of estimation of distribution algorithms to deal with the
problem. Furthermore, we investigate how the regularities of the braid
optimization problem can be translated into statistical regularities by means
of the Boltzmann distribution. We show that our best algorithm is able to
produce many solutions that approximates the target gate with an accuracy in
the order of , and have lengths up to 9 times shorter than those
expected from braids of the same accuracy obtained with other methods.Comment: 9 pages,7 figures. Accepted at SEAL 201
Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates
We study the effect of spin-orbit coupling on quantum gates produced by
pulsing the exchange interaction between two single electron quantum dots.
Spin-orbit coupling enters as a small spin precession when electrons tunnel
between dots. For adiabatic pulses the resulting gate is described by a unitary
operator acting on the four-dimensional Hilbert space of two qubits. If the
precession axis is fixed, time-symmetric pulsing constrains the set of possible
gates to those which, when combined with single qubit rotations, can be used in
a simple CNOT construction. Deviations from time-symmetric pulsing spoil this
construction. The effect of time asymmetry is studied by numerically
integrating the Schr\"odinger equation using parameters appropriate for GaAs
quantum dots. Deviations of the implemented gate from the desired form are
shown to be proportional to dimensionless measures of both spin-orbit coupling
and time asymmetry of the pulse.Comment: 10 pages, 3 figure
Lieb-Schultz-Mattis in Higher Dimensions
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional
spin systems is shown. The physical motivation for the result is that such spin
systems typically either have long-range order, in which case there are gapless
modes, or have only short-range correlations, in which case there are
topological excitations. The result uses a set of loop operators, analogous to
those used in gauge theories, defined in terms of the spin operators of the
theory. We also obtain various cluster bounds on expectation values for gapped
systems. These bounds are used, under the assumption of a gap, to rule out the
first case of long-range order, after which we show the existence of a
topological excitation. Compared to the ground state, the topologically excited
state has, up to a small error, the same expectation values for all operators
acting within any local region, but it has a different momentum.Comment: 14 pages, 3 figures, final version in pres
Superconductivity by long-range color magnetic interaction in high-density quark matter
We argue that in quark matter at high densities, the color magnetic field
remains unscreened and leads to the phenomenon of color superconductivity.
Using the renormalization group near the Fermi surface, we find that the
long-range nature of the magnetic interaction changes the asymptotic behavior
of the gap at large chemical potential qualitatively. We find
, where is the
small gauge coupling. We discuss the possibility of breaking rotational
symmetry by the formation of a condensate with nonzero angular momentum, as
well as interesting parallels to some condensed matter systems with long-range
forces.Comment: 14 pages, REVTEX, uses eps
Double-Layer Systems at Zero Magnetic Field
We investigate theoretically the effects of intralayer and interlayer
exchange in biased double-layer electron and hole systems, in the absence of a
magnetic field. We use a variational Hartree-Fock-like approximation to analyze
the effects of layer separation, layer density, tunneling, and applied gate
voltages on the layer densities and on interlayer phase coherence. In agreement
with earlier work, we find that for very small layer separations and low layer
densities, an interlayer-correlated ground state possessing spontaneous
interlayer coherence (SILC) is obtained, even in the absence of interlayer
tunneling. In contrast to earlier work, we find that as a function of total
density, there exist four, rather than three, distinct noncrystalline phases
for balanced double-layer systems without interlayer tunneling. The newly
identified phase exists for a narrow range of densities and has three
components and slightly unequal layer densities, with one layer being spin
polarized, and the other unpolarized. An additional two-component phase is also
possible in the presence of sufficiently strong bias or tunneling. The
lowest-density SILC phase is the fully spin- and pseudospin-polarized
``one-component'' phase discussed by Zheng {\it et al.} [Phys. Rev. B {\bf 55},
4506 (1997)]. We argue that this phase will produce a finite interlayer Coulomb
drag at zero temperature due to the SILC. We calculate the particle densities
in each layer as a function of the gate voltage and total particle density, and
find that interlayer exchange can reduce or prevent abrupt transfers of charge
between the two layers. We also calculate the effect of interlayer exchange on
the interlayer capacitance.Comment: 35 pages, 19 figures included. To appear in PR
String order in spin liquid phases of spin ladders
Two-leg spin ladders have a rich phase diagram if rung, diagonal and
plaquette couplings are allowed for. Among the possible phases there are two
Haldane-type spin liquid phases without local order parameter, which differ,
however, in the topology of the short range valence bonds. We show that these
phases can be distinguished numerically by two different string order
parameters. We also point out that long range string- and dimer orders can
coexist