2,778 research outputs found
Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks
We review here some general properties of antiferromagnetic Heisenberg spin
chains, emphasizing and discussing the role of hidden symmetries in the
classification of the various phases of the models. We present also some recent
results that have been obtained with a combined use of Conformal Field Theory
and of numerical Density Matrix Renormalization Group techniques.Comment: To be published in the proceedings of the XIII Conference on
"Symmetries in Physics", held in Bregenz (Voralberg, Austria), 21-24/7/2003.
Plain LaTeX2e, 4 EPS figure
Effective mapping of spin-1 chains onto integrable fermionic models. A study of string and Neel correlation functions
We derive the dominant contribution to the large-distance decay of
correlation functions for a spin chain model that exhibits both Haldane and
Neel phases in its ground state phase diagram. The analytic results are
obtained by means of an approximate mapping between a spin-1 anisotropic
Hamiltonian onto a fermionic model of noninteracting Bogolioubov quasiparticles
related in turn to the XY spin-1/2 chain in a transverse field. This approach
allows us to express the spin-1 string operators in terms of fermionic
operators so that the dominant contribution to the string correlators at large
distances can be computed using the technique of Toeplitz determinants. As
expected, we find long-range string order both in the longitudinal and in the
transverse channel in the Haldane phase, while in the Neel phase only the
longitudinal order survives. In this way, the long-range string order can be
explicitly related to the components of the magnetization of the XY model.
Moreover, apart from the critical line, where the decay is algebraic, we find
that in the gapped phases the decay is governed by an exponential tail
multiplied by algebraic factors. As regards the usual two points correlation
functions, we show that the longitudinal one behaves in a 'dual' fashion with
respect to the transverse string correlator, namely both the asymptotic values
and the decay laws exchange when the transition line is crossed. For the
transverse spin-spin correlator, we find a finite characteristic length which
is an unexpected feature at the critical point. We also comment briefly the
entanglement features of the original system versus those of the effective
model. The goodness of the approximation and the analytical predictions are
checked versus density-matrix renormalization group calculations.Comment: 28 pages, plain LaTeX, 2 EPS figure
The resolution of whole Earth seismic tomographic models
We evaluate the resolution of whole Earth structure achieved by compressional wave traveltime data from the International Seismological Centre (ISC); the measure of resolution we employ, provided by the direct calculation of the model resolution matrix, is more rigorous than the traditional (and computationally cheaper) one obtained through synthetic/checkerboard tests. Our work completes the introductive study of Boschi (2003), where only mantle models derived with a very simple regularization scheme were considered. Here, we expand Boschi's database with measurements of compressional waves reflected by, or refracted through, the Earth's core-mantle boundary (CMB) and core. In analogy with the work of Soldati et al. (2003), we treat CMB topography and heterogeneous outer core structure as free parameters of our inversions; analysing model resolution matrices, we attempt to explain the known discrepancy between deep Earth structure mapped by seismic waves reflected and refracted by the cor
Using the Post—Widder formula to compute the Earth's viscoelastic Love numbers
The post-glacial or post-seismic relaxation of a Maxwell viscoelastic earth, 1-D or slightly laterally heterogeneous, can be calculated in a normal-mode approach, based on an application of the propagator technique. This semi-analytical approach, widely documented in the literature, allows to compute the response of an earth model whose rheological parameters vary quite strongly with depth, at least as accurately and efficiently as by 1-D numerical integration (Runge-Kutta). Its main drawback resides in the need to identify the roots of a secular polynomial, introduced after reformulating the problem in the Laplace domain, and required to transform the solution back to the time domain. Root finding becomes increasingly difficult, and ultimately unaffordable, as the complexity of rheological profiles grows: the secular polynomial gradually gets more ill behaved, and a larger number of more and more closely spaced roots is to be found. Here, we apply the propagator method to solve the Earth's viscoelastic momentum equation, like in the above-mentioned normal-mode framework, but bypass root finding, using, instead, the Post-Widder formula to transform the solution, found again in the Laplace domain, back to the time domain. We test our method against earlier normal-mode results, and prove its effectiveness in modelling the relaxation of earth models with extremely complex rheological profile
Gauge/string duality and scalar glueball mass ratios
It has been shown by Polchinski and Strassler that the scaling of high energy
QCD scattering amplitudes can be obtained from string theory. They considered
an AdS slice as an approximation for the dual space of a confining gauge
theory. Here we use this approximation to estimate in a very simple way the
ratios of scalar glueball masses imposing Dirichlet boundary conditions on the
string dilaton field. These ratios are in good agreement with the results in
the literature. We also find that they do not depend on the size of the slice.Comment: 5 pages, no figures. References updated. Version published in JHE
Stable particles in anisotropic spin-1 chains
Motivated by field-theoretic predictions we investigate the stable
excitations that exist in two characteristic gapped phases of a spin-1 model
with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a
region close to the phase boundary where a stable breather exists besides the
stable particles, that form the Haldane triplet at the Heisenberg isotropic
point. The numerical data, obtained by means of the Density Matrix
Renormalization Group, confirm this picture in the so-called large-D phase for
which we give also a quantitative analysis of the bound states using standard
perturbation theory. However, the situation turns out to be considerably more
intricate in the Haldane phase where, to the best of our data, we do not
observe stable breathers contrarily to what could be expected from the
sine-Gordon model, but rather only the three modes predicted by a novel
anisotropic extension of the Non-Linear Sigma Model studied here by means of a
saddle-point approximation.Comment: 8 pages, 7 eps figures, svjour clas
Multiple resolution surface wave tomography: the Mediterranean basin
From a large set of fundamental-mode surface wave phase velocity observations, we map the transversely isotropic lateral heterogeneities in the upper-mantle shear velocity structure. We design a multiple resolution inversion procedure, which allows us to parametrize any selected region more finely than the rest of the globe. We choose, as a high-resolution region, the upper mantle underlying the Mediterranean basin. We formulate the inverse problem as in a previous paper by Boschi & Ekström, calculating regional JWKB (Jeffreys-Wentzel-Kramers-Brillouin) surface wave sensitivity kernels for each pixel of a 2°× 2° starting model, including the high-resolution global crustal map Crust 2.0. We find that the available surface wave data can resolve the most important geophysical features of the region of interest, providing a reliable image of intermediate spatial wavelengt
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