462 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
Effects of nanoscale spatial inhomogeneity in strongly correlated systems
We calculate ground-state energies and density distributions of Hubbard
superlattices characterized by periodic modulations of the on-site interaction
and the on-site potential. Both density-matrix renormalization group and
density-functional methods are employed and compared. We find that small
variations in the on-site potential can simulate, cancel, or even
overcompensate effects due to much larger variations in the on-site interaction
. Our findings highlight the importance of nanoscale spatial inhomogeneity
in strongly correlated systems, and call for reexamination of model
calculations assuming spatial homogeneity.Comment: 5 pages, 1 table, 4 figures, to appear in PR
Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid
A simple, physically motivated, scaling hypothesis, which becomes exact in
important limits, yields estimates for the ground-state energy of large,
composed, systems in terms of the ground-state energy of its building blocks.
The concept is illustrated for the electron liquid, and the Hubbard model. By
means of this scaling argument the energy of the one-dimensional half-filled
Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining
quantitative agreement with the exact one-dimensional Bethe-Ansatz solution,
and the energies of the two- and three-dimensional half-filled Hubbard models
are estimated from the one-dimensional energy, recovering exact results for
and and coming close to Quantum Monte Carlo data for
intermediate .Comment: 3 figure
BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation
We investigate the BCS and generalized BCS theories in the relativistic
quantum field theory. We select the gauge freedom as U(1), and introduce a
BCS-type effective attractive interaction. After introducing the Gor'kov
formalism and performing the group theoretical consideration of the mean
fields, we solve the relativistic Gor'kov equation and obtain the Green's
functions in analytical forms. We obtain various types of gap equations.Comment: 31 page
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
Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory
Thermodynamics provides a transparent definition of the free energy of
density functional theory (DFT), and of its derivatives - the potentials, at
finite temperatures T. By taking the T to 0 limit, it is shown here that both
DFT and spin-dependent DFT (for ground states) suffer from precisely the same
benign ambiguities: (a) charge and spin quantization lead to "up to a constant"
indeterminacies in the potential and the magnetic field respectively, and (b)
the potential in empty subspaces is undetermined but irrelevant. Surprisingly,
these simple facts were inaccessible within the standard formulation, leading
to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.
Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
By shifting the reference system for the local-density approximation (LDA)
from the electron gas to other model systems one obtains a new class of density
functionals, which by design account for the correlations present in the chosen
reference system. This strategy is illustrated by constructing an explicit LDA
for the one-dimensional Hubbard model. While the traditional {\it ab initio}
LDA is based on a Fermi liquid (the electron gas), this one is based on a
Luttinger liquid. First applications to inhomogeneous Hubbard models, including
one containing a localized impurity, are reported.Comment: 4 pages, 4 figures (final version, contains additional applications
and discussion; accepted by Phys. Rev. Lett.
Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems
Current-carrying and superconducting systems can be treated within
density-functional theory if suitable additional density variables (the current
density and the superconducting order parameter, respectively) are included in
the density-functional formalism. Here we show that the corresponding conjugate
potentials (vector and pair potentials, respectively) are {\it not} uniquely
determined by the densities. The Hohenberg-Kohn theorem of these generalized
density-functional theories is thus weaker than the original one. We give
explicit examples and explore some consequences.Comment: revised version (typos corrected, some discussion added) to appear in
Phys. Rev.
Interaction Between Superconducting and Ferromagnetic Order Parameters in Graphite-Sulfur Composites
The superconductivity of graphite-sulfur composites is highly anisotropic and
associated with the graphite planes. The superconducting state coexists with
the ferromagnetism of pure graphite, and a continuous crossover from
superconducting to ferromagnetic-like behavior could be achieved by increasing
the magnetic field or the temperature. The angular dependence of the magnetic
moment m(alpha) provides evidence for an interaction between the ferromagnetic
and the superconducting order parameters.Comment: 11 pages, 4 figures, to be published in Phys. Rev.
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