3,967 research outputs found
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
Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group
A useful concept for finding numerically the dominant correlations of a given
ground state in an interacting quantum lattice system in an unbiased way is the
correlation density matrix. For two disjoint, separated clusters, it is defined
to be the density matrix of their union minus the direct product of their
individual density matrices and contains all correlations between the two
clusters. We show how to extract from the correlation density matrix a general
overview of the correlations as well as detailed information on the operators
carrying long-range correlations and the spatial dependence of their
correlation functions. To determine the correlation density matrix, we
calculate the ground state for a class of spinless extended Hubbard models
using the density matrix renormalization group. This numerical method is based
on matrix product states for which the correlation density matrix can be
obtained straightforwardly. In an appendix, we give a detailed tutorial
introduction to our variational matrix product state approach for ground state
calculations for 1- dimensional quantum chain models. We show in detail how
matrix product states overcome the problem of large Hilbert space dimensions in
these models and describe all techniques which are needed for handling them in
practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic
Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime
We show that in the sudden expansion of a spin-balanced two-component Fermi
gas into an empty optical lattice induced by releasing particles from a trap,
over a wide parameter regime, the radius of the particle cloud grows
linearly in time. This allow us to define the expansion velocity from
. The goal of this work is to clarify the dependence of the
expansion velocity on the initial conditions which we establish from
time-dependent density matrix renormalization group simulations, both for a box
trap and a harmonic trap. As a prominent result, the presence of a
Mott-insulating region leaves clear fingerprints in the expansion velocity. Our
predictions can be verified in experiments with ultra-cold atoms.Comment: 8 pages 10 figures, version as published with minor stylistic change
Neurophysiology
Contains reports on three research projects.National Institutes of Health (Grant 5 ROl NB-04985-04)U. S. Air Force (Aerospace Medical Division) under Contract AF33(615)-3885Bioscience Division of National Aeronautics and Space Administration through Contract NSR 22-009-13
From density-matrix renormalization group to matrix product states
In this paper we give an introduction to the numerical density matrix
renormalization group (DMRG) algorithm, from the perspective of the more
general matrix product state (MPS) formulation. We cover in detail the
differences between the original DMRG formulation and the MPS approach,
demonstrating the additional flexibility that arises from constructing both the
wavefunction and the Hamiltonian in MPS form. We also show how to make use of
global symmetries, for both the Abelian and non-Abelian cases.Comment: Numerous small changes and clarifications, added a figur
On the Nature of Precursors in the Radio Pulsar Profiles
In the average profiles of several radio pulsars, the main pulse is
accompanied by the preceding component. This so called precursor is known for
its distinctive polarization, spectral, and fluctuation properties. Recent
single-pulse observations hint that the sporadic activity at the extreme
leading edge of the pulse may be prevalent in pulsars. We for the first time
propose a physical mechanism of this phenomenon. It is based on the induced
scattering of the main pulse radiation into the background. We show that the
scattered component is directed approximately along the ambient magnetic field
and, because of rotational aberration in the scattering region, appears in the
pulse profile as a precursor to the main pulse. Our model naturally explains
high linear polarization of the precursor emission, its spectral and
fluctuation peculiarities as well as suggests a specific connection between the
precursor and the main pulse at widely spaced frequencies. This is believed to
stimulate multifrequency single-pulse studies of intensity modulation in
different pulsars.Comment: 5 pages, no figures. Accepted for publication in MNRAS Letter
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
The Tajmar effect from quantised inertia
The Tajmar anomaly is an unexplained acceleration observed by gyroscopes
close to, but isolated from, rotating rings cooled to 5K. The observed ratio
between the gyroscope and ring accelerations was 3+/-1.2*10^-8 for clockwise
rotations and about half this size for anticlockwise ones. Here, this anomaly
is predicted using a new model that assumes that the inertial mass of the
gyroscope is caused by Unruh radiation that appears as the ring and the fixed
stars accelerate relative to it, and that this radiation is subject to a
Hubble-scale Casimir effect. The model predicts that the sudden acceleration of
the ring causes a slight increase in the inertial mass of the gyroscope, and,
to conserve momentum the gyroscope must move with the ring with an acceleration
ratio of 2.67+/-0.24*10^-8 for clockwise rotations and 1.34+/-0.12*10^-8 for
anticlockwise ones, in agreement with the observations. The model predicts that
in the southern hemisphere the anomaly should be larger for anticlockwise
rotations instead, and that with a significant reduction of the mass of the
disc, the decay of the effect with vertical distance should become measurable.Comment: 9 pages, 1 figure. Accepted by EPL on the 16th June, 201
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