9,980 research outputs found
Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin- Models
We apply the microscopic coupled-cluster method (CCM) to the spin-
models on both the one-dimensional chain and the two-dimensional square
lattice. Based on a systematic approximation scheme of the CCM developed by us
previously, we carry out high-order {\it ab initio} calculations using
computer-algebraic techniques. The ground-state properties of the models are
obtained with high accuracy as functions of the anisotropy parameter.
Furthermore, our CCM analysis enables us to study their quantum critical
behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon
request. UMIST Preprint MA-000-000
Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
We present a method for the direct calculation of the spin stiffness by means
of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on
the square, the triangular and the cubic lattices we calculate the stiffness in
high orders of approximation. For the square and the cubic lattices our results
are in very good agreement with the best results available in the literature.
For the triangular lattice our result is more precise than any other result
obtained so far by other approximate method.Comment: 5 pages, 2 figure
Oscillating elastic defects: competition and frustration
We consider a dynamical generalization of the Eshelby problem: the strain
profile due to an inclusion or "defect" in an isotropic elastic medium. We show
that the higher the oscillation frequency of the defect, the more localized is
the strain field around the defect. We then demonstrate that the qualitative
nature of the interaction between two defects is strongly dependent on
separation, frequency and direction, changing from "ferromagnetic" to
"antiferromagnetic" like behavior. We generalize to a finite density of defects
and show that the interactions in assemblies of defects can be mapped to XY
spin-like models, and describe implications for frustration and
frequency-driven pattern transitions.Comment: 4 pages, 5 figure
The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice
By means of numerical simulations, we demonstrate that ac field can support
stably moving collective nonlinear excitations in the form of dislocations
(topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with
weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys.
Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations
turns out to be virtually impossible; however, they can be generated initially
in the lattice subject to an auxiliary spatial modulation of the on-site
potential strength. Gradually relaxing the modulation, we are able to get the
stable moving dislocations in the uniform FK lattice with the periodic boundary
conditions, provided that the driving frequency is close to the gap frequency
of the linear excitations in the uniform lattice. The excitations have a large
and noninteger index of commensurability with the lattice (suggesting that its
actual value is irrational). The simulations reveal two different types of the
moving dislocations: broad ones, that extend, roughly, to half the full length
of the periodic lattice (in that sense, they cannot be called solitons), and
localized soliton-like dislocations, that can be found in an excited state,
demonstrating strong persistent internal vibrations. The minimum (threshold)
amplitude of the driving force necessary to support the traveling excitation is
found as a function of the friction coefficient. Its extrapolation suggests
that the threshold does not vanish at the zero friction, which may be explained
by radiation losses. The moving dislocation can be observed experimentally in
an array of coupled small Josephson junctions in the form of an {\it inverse
Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias
current.Comment: Plain Latex, 13 pages + 9 PostScript figures. to appear on Journal of
Physics: condensed matte
An extension of the coupled-cluster method: A variational formalism
A general quantum many-body theory in configuration space is developed by
extending the traditional coupled cluter method (CCM) to a variational
formalism. Two independent sets of distribution functions are introduced to
evaluate the Hamiltonian expectation. An algebraic technique for calculating
these distribution functions via two self-consistent sets of equations is
given. By comparing with the traditional CCM and with Arponen's extension, it
is shown that the former is equivalent to a linear approximation to one set of
distribution functions and the later is equivalent to a random-phase
approximation to it. In additional to these two approximations, other
higher-order approximation schemes within the new formalism are also discussed.
As a demonstration, we apply this technique to a quantum antiferromagnetic spin
model.Comment: 15 pages. Submitted to Phys. Rev.
Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation
We investigate the thermal equilibrium properties of kinks in a classical
\F^4 field theory in dimensions. From large scale Langevin simulations
we identify the temperature below which a dilute gas description of kinks is
valid. The standard dilute gas/WKB description is shown to be remarkably
accurate below this temperature. At higher, ``intermediate'' temperatures,
where kinks still exist, this description breaks down. By introducing a double
Gaussian variational ansatz for the eigenfunctions of the statistical transfer
operator for the system, we are able to study this region analytically. In
particular, our predictions for the number of kinks and the correlation length
are in agreement with the simulations. The double Gaussian prediction for the
characteristic temperature at which the kink description ultimately breaks down
is also in accord with the simulations. We also analytically calculate the
internal energy and demonstrate that the peak in the specific heat near the
kink characteristic temperature is indeed due to kinks. In the neighborhood of
this temperature there appears to be an intricate energy sharing mechanism
operating between nonlinear phonons and kinks.Comment: 28 pages (8 Figures not included, hard-copies available), Latex,
LA-UR-93-276
Statistical Mechanics of Kinks in (1+1)-Dimensions
We investigate the thermal equilibrium properties of kinks in a classical
field theory in dimensions. The distribution function, kink
density, and correlation function are determined from large scale simulations.
A dilute gas description of kinks is shown to be valid below a characteristic
temperature. A double Gaussian approximation to evaluate the eigenvalues of the
transfer operator enables us to extend the theoretical analysis to higher
temperatures where the dilute gas approximation fails. This approach accurately
predicts the temperature at which the kink description breaks down.Comment: 8 pages, Latex (4 figures available on request), LA-UR-92-399
Unitarity potentials and neutron matter at the unitary limit
We study the equation of state of neutron matter using a family of unitarity
potentials all of which are constructed to have infinite scattering
lengths . For such system, a quantity of much interest is the ratio
where is the true ground-state energy of the system,
and is that for the non-interacting system. In the limit of
, often referred to as the unitary limit, this ratio is
expected to approach a universal constant, namely . In the
present work we calculate this ratio using a family of hard-core
square-well potentials whose can be exactly obtained, thus enabling us to
have many potentials of different ranges and strengths, all with infinite
. We have also calculated using a unitarity CDBonn potential
obtained by slightly scaling its meson parameters. The ratios given by
these different unitarity potentials are all close to each other and also
remarkably close to 0.44, suggesting that the above ratio is indifferent
to the details of the underlying interactions as long as they have infinite
scattering length. A sum-rule and scaling constraint for the renormalized
low-momentum interaction in neutron matter at the unitary limit is discussed.Comment: 7.5 pages, 7 figure
Dynamic charge correlations near the Peierls transition
The quantum phase transition between a repulsive Luttinger liquid and an
insulating Peierls state is studied in the framework of the one-dimensional
spinless Holstein model. We focus on the adiabatic regime but include the full
quantum dynamics of the phonons. Using continuous-time quantum Monte Carlo
simulations, we track in particular the dynamic charge structure factor and the
single-particle spectrum across the transition. With increasing electron-phonon
coupling, the dynamic charge structure factor reveals the emergence of a charge
gap, and a clear signature of phonon softening at the zone boundary. The
single-particle spectral function evolves continuously across the transition.
Hybridization of the charge and phonon modes of the Luttinger liquid
description leads to two modes, one of which corresponds to the coherent
polaron band. This band acquires a gap upon entering the Peierls phase, whereas
the other mode constitutes the incoherent, high-energy spectrum with backfolded
shadow bands. Coherent polaronic motion is a direct consequence of quantum
lattice fluctuations. In the strong-coupling regime, the spectrum is described
by the static, mean-field limit. Importantly, whereas finite electron density
in general leads to screening of polaron effects, the latter reappear at half
filling due to charge ordering and lattice dimerization.Comment: 8 pages, 7 figures, final versio
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