34 research outputs found
Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
Simple analytical parametrizations for the ground-state energy of the
one-dimensional repulsive Hubbard model are developed. The charge-dependence of
the energy is parametrized using exact results extracted from the Bethe-Ansatz.
The resulting parametrization is shown to be in better agreement with highly
precise data obtained from fully numerical solution of the Bethe-Ansatz
equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402
(2003)]. Unlike these earlier proposals, the present parametrization correctly
predicts a positive Mott gap at half filling for any U>0. The construction is
extended to spin-dependent phenomena by parametrizing the
magnetization-dependence of the ground-state energy using further exact results
and numerical benchmarking. Lastly, the parametrizations developed for the
spatially uniform model are extended by means of a simple local-density-type
approximation to spatially inhomogeneous models, e.g., in the presence of
impurities, external fields or trapping potentials. Results are shown to be in
excellent agreement with independent many-body calculations, at a fraction of
the computational cost.Comment: New Journal of Physics, accepte
Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins
A combined analytical and numerical study is performed of the mapping between
strongly interacting fermions and weakly interacting spins, in the framework of
the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models
in the thermodynamic limit the mapping is thoroughly understood, we here focus
on aspects that become relevant in spatially inhomogeneous situations, such as
the effect of boundaries, impurities, superlattices and interfaces. We consider
parameter regimes that are relevant for traditional applications of these
models, such as electrons in cuprates and manganites, and for more recent
applications to atoms in optical lattices. The rate of the mapping as a
function of the interaction strength is determined from the Bethe-Ansatz for
infinite systems and from numerical diagonalization for finite systems. We show
analytically that if translational symmetry is broken through the presence of
impurities, the mapping persists and is, in a certain sense, as local as
possible, provided the spin-spin interaction between two sites of the
Heisenberg model is calculated from the harmonic mean of the onsite Coulomb
interaction on adjacent sites of the Hubbard model. Numerical calculations
corroborate these findings also in interfaces and superlattices, where
analytical calculations are more complicated.Comment: 7 pages, 6 figure
Surveying the solar system by measuring angles and times: from the solar density to the gravitational constant
A surprisingly large amount of information on our solar system can be gained
from simple measurements of the apparent angular diameters of the sun and the
moon. This information includes the average density of the sun, the distance
between earth and moon, the radius of the moon, and the gravitational constant.
In this note it is described how these and other quantities can be obtained by
simple earthbound measurements of angles and times only, without using any
explicit information on distances between celestial bodies. The pedagogical and
historical aspects of these results are also discussed briefly.Comment: 12 pges, one figur