3,859 research outputs found
Testing quantised inertia on galactic scales
Galaxies and galaxy clusters have rotational velocities apparently too fast
to allow them to be gravitationally bound by their visible matter. This has
been attributed to the presence of invisible (dark) matter, but so far this has
not been directly detected. Here, it is shown that a new model that modifies
inertial mass by assuming it is caused by Unruh radiation, which is subject to
a Hubble-scale (Theta) Casimir effect predicts the rotational velocity (v) to
be: v^4=2GMc^2/Theta (the Tully-Fisher relation) where G is the gravitational
constant, M is the baryonic mass and c is the speed of light. The model
predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy
clusters, within error bars, without dark matter or adjustable parameters, and
makes a prediction that local accelerations should remain above 2c^2/Theta at a
galaxy's edge.Comment: 7 pages, 1 figure. Accepted for publication in Astrophysics and Space
Science on 27/7/201
Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux
We perform a density-matrix renormalization-group study of strongly
interacting bosons on a three-leg ladder in the presence of a homogeneous flux.
Focusing on one-third filling, we explore the phase diagram in dependence of
the magnetic flux and the inter-leg tunneling strength. We find several phases
including a Meissner phase, vortex liquids, a vortex lattice, as well as a
staggered-current phase. Moreover, there are regions where the chiral current
reverses its direction, both in the Meissner and in the staggered-current
phase. While the reversal in the latter case can be ascribed to spontaneous
breaking of translational invariance, in the first it stems from an effective
flux increase in the rung direction. Interactions are a necessary ingredient to
realize either type of chiral-current reversal
A Strictly Single-Site DMRG Algorithm with Subspace Expansion
We introduce a strictly single-site DMRG algorithm based on the subspace
expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS
basis enrichment method is sufficient to avoid local minima during the
optimisation, similarly to the density matrix perturbation method, but
computationally cheaper. Each application of to in the
central eigensolver is reduced in cost for a speed-up of ,
with the physical site dimension. Further speed-ups result from cheaper
auxiliary calculations and an often greatly improved convergence behaviour.
Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard
model compared to the previous single-site method and by up to a factor of 3.9
compared to two-site DMRG. The method is compatible with real-space
parallelisation and non-abelian symmetries.Comment: 9 pages, 6 figures; added comparison with two-site DMR
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for
fermions with positive weights. In the example of the Hubbard model close to
half filling it fails to reproduce all the symmetries of the ground state
leading to systematic errors at low temperatures. In a previous work [Phys.
Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by
projecting the density matrix obtained from the simulation onto the ground
state symmetry sector. For ground state properties, the accuracy of this method
depends on a {\it large overlap} between the GQMC and exact density matrices.
Thus, the method is not rigorously exact. We present the limits of the approach
by a systematic study of the method for 2 and 3 leg Hubbard ladders for
different fillings and on-site repulsion strengths. We show several indications
that the systematic errors stem from non-vanishing boundary terms in the
partial integration step in the derivation of the Fokker-Planck equation.
Checking for spiking trajectories and slow decaying probability distributions
provides an important test of the reliability of the results. Possible
solutions to avoid boundary terms are discussed. Furthermore we compare results
obtained from two different sampling methods: Reconfiguration of walkers and
the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl
Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study
We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with
anisotropic exchange interactions in an external magnetic field, using the
density matrix renormalization group method. We show that an easy-axis
anisotropy enhances the tendency towards multimagnon bound states, while an
easy-plane anisotropy favors chirally ordered phases. In particular, a moderate
easy-plane anisotropy gives rise to a quantum phase transition at intermediate
magnetization. We argue that this transition is related to the finite-field
phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.Comment: The final published versio
Spectral functions and time evolution from the Chebyshev recursion
We link linear prediction of Chebyshev and Fourier expansions to analytic
continuation. We push the resolution in the Chebyshev-based computation of
many-body spectral functions to a much higher precision by deriving a
modified Chebyshev series expansion that allows to reduce the expansion order
by a factor . We show that in a certain limit the Chebyshev
technique becomes equivalent to computing spectral functions via time evolution
and subsequent Fourier transform. This introduces a novel recursive time
evolution algorithm that instead of the group operator only involves
the action of the generator . For quantum impurity problems, we introduce an
adapted discretization scheme for the bath spectral function. We discuss the
relevance of these results for matrix product state (MPS) based DMRG-type
algorithms, and their use within dynamical mean-field theory (DMFT). We present
strong evidence that the Chebyshev recursion extracts less spectral information
from than time evolution algorithms when fixing a given amount of created
entanglement.Comment: 12 pages + 6 pages appendix, 11 figure
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
We develop variational matrix product state (MPS) methods with symmetries to
determine dispersion relations of one dimensional quantum lattices as a
function of momentum and preset quantum number. We test our methods on the XXZ
spin chain, the Hubbard model and a non-integrable extended Hubbard model, and
determine the excitation spectra with a precision similar to the one of the
ground state. The formulation in terms of quantum numbers makes the topological
nature of spinons and holons very explicit. In addition, the method also
enables an easy and efficient direct calculation of the necessary magnetic
field or chemical potential required for a certain ground state magnetization
or particle density.Comment: 13 pages, 4 pages appendix, 8 figure
Imaginary-time matrix product state impurity solver for dynamical mean-field theory
We present a new impurity solver for dynamical mean-field theory based on
imaginary-time evolution of matrix product states. This converges the
self-consistency loop on the imaginary-frequency axis and obtains
real-frequency information in a final real-time evolution. Relative to
computations on the real-frequency axis, required bath sizes are much smaller
and less entanglement is generated, so much larger systems can be studied. The
power of the method is demonstrated by solutions of a three band model in the
single and two-site dynamical mean-field approximation. Technical issues are
discussed, including details of the method, efficiency as compared to other
matrix product state based impurity solvers, bath construction and its relation
to real-frequency computations and the analytic continuation problem of quantum
Monte Carlo, the choice of basis in dynamical cluster approximation, and
perspectives for off-diagonal hybridization functions.Comment: 8 pages + 4 pages appendix, 9 figure
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