1,642 research outputs found
Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain
In order to study the interplay between Kondo and
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, we calculate the spin-spin
correlation functions between two Kondo impurities coupled to different sites
of a half-filled open Hubbard chain. Using the density-matrix renormalization
group (DMRG), we re-examine the exponents for the power-law decay of the
correlation function between the two impurity spins as a function of the
antiferromagnetic coupling J, the Hubbard interaction U, and the distance R
between the impurities. The exponents for finite systems obtained in this work
deviate from previously published DMRG calculations. We furthermore show that
the long-distance behavior of the exponents is the same for impurities coupled
to the bulk or to both ends of the chain. We note that a universal exponent for
the asymptotic behavior cannot be extracted from these finite-size systems with
open boundary conditions.Comment: 8 pages, 10 figures; v2: final version, references and Fig. 8 adde
Features of spin-charge separation in the equilibrium conductance through finite rings
We calculate the conductance through rings with few sites described by
the model, threaded by a magnetic flux and weakly coupled to
conducting leads at two arbitrary sites. The model can describe a circular
array of quantum dots with large charging energy in comparison with the
nearest-neighbor hopping . We determine analytically the particular values
of for which a depression of the transmittance is expected as a
consequence of spin-charge separation. We show numerically that the equilibrium
conductance at zero temperature is depressed at those particular values of
for most systems, in particular at half filling, which might be easier
to realize experimentally.Comment: 8 pages, 7 figure
Primate Numerical Competence: Contributions Toward Understanding Nonhuman Cognition
Nonhuman primates represent the most significant extant species for comparative studies of cognition, including such complex phenomena as numerical competence, among others. Studies of numerical skills in monkeys and apes have a long, though somewhat sparse history, although questions for current empirical studies remain of great interest to several fields, including comparative, developmental, and cognitive psychology; anthropology; ethology; and philosophy, to name a few. In addition to demonstrated similarities in complex information processing, empirical studies of a variety of potential cognitive limitations or constraints have provided insights into similarities and differences across the primate order, and continue to offer theoretical and pragmatic directions for future research. An historical overview of primate numerical studies is presented, as well as a summary of the 17-year research history, including recent findings, of the Comparative Cognition Project at The Ohio State University Chimpanzee Center. Overall, the archival literature on number-related skills and counting in nonhuman primates offers important implications for revising our thinking about comparative neuroanatomy, cross-species (human/ape) cognitive similarities and differences, and the evolution of cognition represented by the primate continuum
Response of finite spin-S Heisenberg chains to local perturbations
We consider the properties of finite isotropic antiferromagnetic Heisenberg
chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few
sites, using White's density matrix renormalization group (DMRG) method. For
the S=1 chain there exists only one length scale in the system which determines
the behavior of the one- and two-point correlation functions both around the
local perturbation and near the free boundary. For the critical,
half-odd-integer spin cases the exponent of the spin-spin correlation function
was found to be , and the exponent of the decay of the site
magnetization around the perturbed site is . Close to a free
boundary, however, the behavior is completely different for S=1/2 and .Comment: 13 pages, 7 figure
Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
The exact amplitude for the asymptotic correlation function in the S=1/2
Heisenberg antiferromagnetic chain is determined: goes to (-1)^r
delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation
functions for small xxz anisotropy and the form of finite-size corrections to
the correlation function are also analysed.Comment: 8 pages, 3 figures, added reference and discussio
Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain
Corrections to the asymptotic correlation function in a Heisenberg spin-1/2
antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a
function of the distance r or the chain size L. This leads to significant
differences with numerical results. We calculate the sub-leading logarithmic
corrections to the finite-size correlation function, using renormalization
group improved perturbation theory, and compare the result with numerical data.Comment: 7 pages Revtex, 3 figure
Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes
We review the theoretical description of spin-orbit scattering and electron
spin resonance in carbon nanotubes. Particular emphasis is laid on the effects
of electron-electron interactions. The spin-orbit coupling is derived, and the
resulting ESR spectrum is analyzed both using the effective low-energy field
theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard
ladders. For single-wall tubes, the field theoretical description predicts a
double peak spectrum linked to the existence of spin-charge separation. The
numerical analysis basically confirms this picture, but also predicts
additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J.
Phys. Cond. Mat., published versio
Uniqueness and Non-uniqueness in the Einstein Constraints
The conformal thin sandwich (CTS) equations are a set of four of the Einstein
equations, which generalize the Laplace-Poisson equation of Newton's theory. We
examine numerically solutions of the CTS equations describing perturbed
Minkowski space, and find only one solution. However, we find {\em two}
distinct solutions, one even containing a black hole, when the lapse is
determined by a fifth elliptic equation through specification of the mean
curvature. While the relationship of the two systems and their solutions is a
fundamental property of general relativity, this fairly simple example of an
elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte
Detection of topological transitions by transport through molecules and nanodevices
We analyze the phase transitions of an interacting electronic system weakly
coupled to free-electron leads by considering its zero-bias conductance. This
is expressed in terms of two effective impurity models for the cases with and
without spin degeneracy. We demonstrate using the half-filled ionic Hubbard
ring that the weight of the first conductance peak as a function of external
flux or of the difference in gate voltages between even and odd sites allows
one to identify the topological charge transition between a correlated
insulator and a band insulator.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let
Two-state behaviour of Kondo trimers
The electronic properties and spectroscopic features of a magnetic trimer
with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at
zero temperature. The substrate density of states is depressed in the trimer
neighbourhood, being exactly zero at the substrate chemical potential. The size
of the resonance strongly depends on the magnetic state of the trimer, and
exhibits a two-state behavior. The geometrical dependence of these results
agree qualitatively with recent experiments and could be reproduced in a
triangular quantum dot arrangement.Comment: 5 pages, including 4 figure
- …