7,451 research outputs found
Phase diagram of the one-dimensional Holstein model of spinless fermions
The one-dimensional Holstein model of spinless fermions interacting with
dispersionless phonons is studied using a new variant of the density matrix
renormalisation group. By examining various low-energy excitations of finite
chains, the metal-insulator phase boundary is determined precisely and agrees
with the predictions of strong coupling theory in the anti-adiabatic regime and
is consistent with renormalisation group arguments in the adiabatic regime. The
Luttinger liquid parameters, determined by finite-size scaling, are consistent
with a Kosterlitz-Thouless transition.Comment: Minor changes. 4 pages, 4 figures. To appear in Physical Review
Letters 80 (1998) 560
Ground-state properties of the One-dimensional Kondo Lattice at partial Band-filling
We compute the magnetic structure factor, the singlet correlation function
and the momentum distribution of the one-dimensional Kondo lattice model at the
density . The density matrix-renormalization group method is used.
We show that in the weak-coupling regime, the ground state is paramagnetic. We
argue that a Luttinger liquid description of the model in this region is
consistent with our calculations . In the strong-coupling regime, the ground
state becomes ferromagnetic. The conduction electrons show a spinless-fermion
like behavior.Comment: 8 pages, Latex, 5 figures included, to be published in PRB (Rapid
Communications
Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System
We use the density matrix renormalization group (DMRG) to map out the ground
state of a XY-spin chain coupled to dispersionless phonons of frequency . We confirm the existence of a critical spin-phonon coupling for the onset of the spin gap bearing the signature of
a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover
when the spin-Peierls gap is of order . In the classical
regime, , the mean-field parameters are strongly renormalized
by non-adiabatic corrections. This is the first application of the DMRG to
phonons.Comment: 10 pages, 5 figures. To be published in PR
Experimental study of digital image processing techniques for LANDSAT data
The author has identified the following significant results. Results are reported for: (1) subscene registration, (2) full scene rectification and registration, (3) resampling techniques, (4) and ground control point (GCP) extraction. Subscenes (354 pixels x 234 lines) were registered to approximately 1/4 pixel accuracy and evaluated by change detection imagery for three cases: (1) bulk data registration, (2) precision correction of a reference subscene using GCP data, and (3) independently precision processed subscenes. Full scene rectification and registration results were evaluated by using a correlation technique to measure registration errors of 0.3 pixel rms thoughout the full scene. Resampling evaluations of nearest neighbor and TRW cubic convolution processed data included change detection imagery and feature classification. Resampled data were also evaluated for an MSS scene containing specular solar reflections
Gravitational waves about curved backgrounds: a consistency analysis in de Sitter spacetime
Gravitational waves are considered as metric perturbations about a curved
background metric, rather than the flat Minkowski metric since several
situations of physical interest can be discussed by this generalization. In
this case, when the de Donder gauge is imposed, its preservation under
infinitesimal spacetime diffeomorphisms is guaranteed if and only if the
associated covector is ruled by a second-order hyperbolic operator which is the
classical counterpart of the ghost operator in quantum gravity. In such a wave
equation, the Ricci term has opposite sign with respect to the wave equation
for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate
the solutions of the two problems, and the algorithm is applied to the case
when the curved background geometry is the de Sitter spacetime. Such vector
wave equations are studied in two different ways: i) an integral
representation, ii) through a solution by factorization of the hyperbolic
equation. The latter method is extended to the wave equation of metric
perturbations in the de Sitter spacetime. This approach is a step towards a
general discussion of gravitational waves in the de Sitter spacetime and might
assume relevance in cosmology in order to study the stochastic background
emerging from inflation.Comment: 17 pages. Misprints amended in Eqs. 50, 54, 55, 75, 7
Gravitational Waves from the Dynamical Bar Instability in a Rapidly Rotating Star
A rapidly rotating, axisymmetric star can be dynamically unstable to an m=2
"bar" mode that transforms the star from a disk shape to an elongated bar. The
fate of such a bar-shaped star is uncertain. Some previous numerical studies
indicate that the bar is short lived, lasting for only a few bar-rotation
periods, while other studies suggest that the bar is relatively long lived.
This paper contains the results of a numerical simulation of a rapidly rotating
gamma=5/3 fluid star. The simulation shows that the bar shape is long lived:
once the bar is established, the star retains this shape for more than 10
bar-rotation periods, through the end of the simulation. The results are
consistent with the conjecture that a star will retain its bar shape
indefinitely on a dynamical time scale, as long as its rotation rate exceeds
the threshold for secular bar instability. The results are described in terms
of a low density neutron star, but can be scaled to represent, for example, a
burned-out stellar core that is prevented from complete collapse by centrifugal
forces. Estimates for the gravitational-wave signal indicate that a dynamically
unstable neutron star in our galaxy can be detected easily by the first
generation of ground based gravitational-wave detectors. The signal for an
unstable neutron star in the Virgo cluster might be seen by the planned
advanced detectors. The Newtonian/quadrupole approximation is used throughout
this work.Comment: Expanded version to be published in Phys. Rev. D: 13 pages, REVTeX,
13 figures, 9 TeX input file
Power laws in a 2-leg ladder of interacting spinless fermions
We use the Density-Matrix Renormalization Group to study the single-particle
and two-particle correlation functions of spinless fermions in the ground state
of a quarter-filled ladder. This ladder consists of two chains having an
in-chain extended Coulomb interaction reaching to third neighbor and coupled by
inter-chain hopping. Within our short numerical coherence lengths, typically
reaching ten to twenty sites, we find a strong renormalization of the
interchain hopping and the existence of a dimensional crossover at smaller
interactions. We also find power exponents for single-particle hopping and
interchain polarization consistent with the single chain. The total charge
correlation function has a larger power exponent and shows signs of a crossover
from incoherent fermion hopping to coherent particle-hole pair motion between
chains. There are no significant excitation energies.Comment: RevTex 4 file, 10 pages, 10 eps figure
Density Matrix Approach to Local Hilbert Space Reduction
We present a density matrix approach for treating systems with a large or
infinite number of degrees of freedom per site with exact diagonalization or
the density matrix renormalization group. The method is demonstrated on the 1D
Holstein model of electrons coupled to Einstein phonons. In this system, two or
three optimized phonon modes per site give results as accurate as with 10-100
bare phonon levels per site.Comment: 4 pages, 4 figure
Phase diagram of a Heisenberg spin-Peierls model with quantum phonons
Using a new version of the density-matrix renormalization group we determine
the phase diagram of a model of an antiferromagnetic Heisenberg spin chain
where the spins interact with quantum phonons. A quantum phase transition from
a gapless spin-fluid state to a gapped dimerized phase occurs at a non-zero
value of the spin-phonon coupling. The transition is in the same universality
class as that of a frustrated spin chain, which the model maps to in the
anti-adiabatic limit. We argue that realistic modeling of known spin-Peierls
materials should include the effects of quantum phonons.Comment: RevTeX, 5 pages, 3 eps figures included using epsf. Improved theories
in adiabatic and non-adiabatic regimes give better agreement with DMRG. This
version accepted in Physical Review Letter
Charge density wave and quantum fluctuations in a molecular crystal
We consider an electron-phonon system in two and three dimensions on square,
hexagonal and cubic lattices. The model is a modification of the standard
Holstein model where the optical branch is appropriately curved in order to
have a reflection positive Hamiltonian. Using infrared bounds together with a
recent result on the coexistence of long-range order for electron and phonon
fields, we prove that, at sufficiently low temperatures and sufficiently strong
electron-phonon coupling, there is a Peierls instability towards a period two
charge-density wave at half-filling. Our results take into account the quantum
fluctuations of the elastic field in a rigorous way and are therefore
independent of any adiabatic approximation. The strong coupling and low
temperature regime found here is independent of the strength of the quantum
fluctuations of the elastic field.Comment: 15 pages, 1 figur
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