12,320 research outputs found
Ground state projection of quantum spin systems in the valence bond basis
A Monte Carlo method for quantum spin systems is formulated in the basis of
valence bond (singlet pair) states. The non-orthogonality of this basis allows
for an efficient importance-sampled projection of the ground state out of an
arbitrary state. The method provides access to resonating valence-bond physics,
enables a direct improved estimator for the singlet-triplet gap, and extends
the class of models that can be studied without negative-sign problems. As a
demonstration, the valence bond distribution in the ground state of the 2D
Heisenberg antiferromagnet is calculated. Generalizations of the method to
fermion systems are also discussed.Comment: 4+ pages, accepted for publication in Phys. Rev. Let
Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
We develop a general approach to the nonequilibrium dynamics of quantum
impurity systems for arbitrary coupling strength. The numerical renormalization
group is used to generate a complete basis set necessary for the correct
description of the time evolution. We benchmark our method with the exact
analytical solution for the resonant-level model. As a first application, we
investigate the equilibration of a quantum dot subject to a sudden change of
the gate voltage and external magnetic field. Two distinct relaxation times are
identified for the spin and charge dynamics.Comment: 5 pages, 5 figure
Magnetic ordering in a doped frustrated spin-Peierls system
Based on a model of a quasi-one dimensional spin-Peierls system doped with
non-magnetic impurities, an effective two-dimensional Hamiltonian of randomly
distributed S=1/2 spins interacting via long-range pair-wise interaction is
studied using a stochastic series expansion quantum Monte Carlo method. The
susceptibility shows Curie-like behavior at the lowest temperatures reached
although the staggered magnetisation is found to be finite for . The
doping dependance of the corresponding three-dimensional Neel temperature is
also computed.Comment: Published version, 4 pages, 5 figure
Topological Optimization of the Evaluation of Finite Element Matrices
We present a topological framework for finding low-flop algorithms for
evaluating element stiffness matrices associated with multilinear forms for
finite element methods posed over straight-sided affine domains. This framework
relies on phrasing the computation on each element as the contraction of each
collection of reference element tensors with an element-specific geometric
tensor. We then present a new concept of complexity-reducing relations that
serve as distance relations between these reference element tensors. This
notion sets up a graph-theoretic context in which we may find an optimized
algorithm by computing a minimum spanning tree. We present experimental results
for some common multilinear forms showing significant reductions in operation
count and also discuss some efficient algorithms for building the graph we use
for the optimization
Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates
We propose to use quantum tomography to characterize the state of a perturbed
Bose-Einstein condensate. We assume knowledge of the number of particles in the
zero-wave number mode and of density distributions in space at different times,
and we treat the condensate in the Bogoliubov approximation. For states that
can be treated with the Gross-Pitaevskii equation, we find that the
reconstructed density operator gives excellent predictions of the second
moments of the atomic creation- and annihilation operators, including the
one-body density matrix. Additional inclusion of the momentum distribution at
one point of time enables somewhat reliable predictions to be made for the
second moments for mixed states, making it possible to distinguish between
coherent and thermal perturbations of the condensate. Finally, we find that
with observation of the zero-wave number mode's anomalous second moment the
reconstructed density operator gives reliable predictions of the second moments
of locally amplitude squeezed states.Comment: 12 pages, 7 figure
Zero-bias conductance in carbon nanotube quantum dots
We present numerical renormalization group calculations for the zero-bias
conductance of quantum dots made from semiconducting carbon nanotubes. These
explain and reproduce the thermal evolution of the conductance for different
groups of orbitals, as the dot-lead tunnel coupling is varied and the system
evolves from correlated Kondo behavior to more weakly correlated regimes. For
integer fillings of an SU(4) model, we find universal scaling
behavior of the conductance that is distinct from the standard SU(2) universal
conductance, and concurs quantitatively with experiment. Our results also agree
qualitatively with experimental differential conductance maps.Comment: 4 pages, 5 figure
Spinful bosons in an optical lattice
We analyze the behavior of cold spin-1 particles with antiferromagnetic
interactions in a one-dimensional optical lattice using density matrix
renormalization group calculations. Correlation functions and the dimerization
are shown and we also present results for the energy gap between ground state
and the spin excited states. We confirm the anticipated phase diagram, with
Mott-insulating regions of alternating dimerized S=1 chains for odd particle
density versus on-site singlets for even density. We find no evidence for any
additional ordered phases in the physically accessible region, however for
sufficiently large spin interaction, on-site singlet pairs dominate leading,
for odd density, to a breakdown of the Mott insulator or, for even density, a
real-space singlet superfluid.Comment: Minor revisions and clarification
Continuous star cluster formation in the spiral NGC 45
We determined ages for 52 star clusters with masses < 10^6 solar masses in
the low surface brightness spiral galaxy NGC 45. Four of these candidates are
old globular clusters located in the bulge. The remaining ones span a large age
range. The cluster ages suggest a continuous star/cluster formation history
without evidence for bursts, consistent with the galaxy being located in a
relatively unperturbed environment in the outskirts of the Sculptor group.Comment: 4 pages, 3 figures. To appear in "Island Universes - Structure and
Evolution of Disk Galaxies", Terschelling (Netherlands), July 200
Wilson chains are not thermal reservoirs
Wilson chains, based on a logarithmic discretization of a continuous
spectrum, are widely used to model an electronic (or bosonic) bath for Kondo
spins and other quantum impurities within the numerical renormalization group
method and other numerical approaches. In this short note we point out that
Wilson chains can not serve as thermal reservoirs as their temperature changes
by a number of order Delta E when a finite amount of energy Delta E is added.
This proves that for a large class of non-equilibrium problems they cannot be
used to predict the long-time behavior.Comment: 2 page
Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations
We perform numerical simulations of the Kelvin-Helmholtz instability in the
mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the
azimuthal--vertical plane of the disk is considered where we include the
Coriolis force and the radial advection of the Keplerian rotation flow. Dust
grains, treated as individual particles, move under the influence of friction
with the gas, while the gas is treated as a compressible fluid. The friction
force from the dust grains on the gas leads to a vertical shear in the gas
rotation velocity. As the particles settle around the mid-plane due to gravity,
the shear increases, and eventually the flow becomes unstable to the
Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when
the vertical settling of the dust is balanced by the turbulent diffusion away
from the mid-plane. The azimuthally averaged state of the self-sustained
Kelvin-Helmholtz turbulence is found to have a constant Richardson number in
the region around the mid-plane where the dust-to-gas ratio is significant.
Nevertheless the dust density has a strong non-axisymmetric component. We
identify a powerful clumping mechanism, caused by the dependence of the
rotation velocity of the dust grains on the dust-to-gas ratio, as the source of
the non-axisymmetry. Our simulations confirm recent findings that the critical
Richardson number for Kelvin-Helmholtz instability is around unity or larger,
rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee
report, most notably that the clumping mechanism has been identified as the
streaming instability of Youdin & Goodman (2005). Movies of the simulations
are still available at http://www.mpia.de/homes/johansen/research_en.ph
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