414 research outputs found
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
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
Density-functional calculation of ionization energies of current-carrying atomic states
Current-density-functional theory is used to calculate ionization energies of
current-carrying atomic states. A perturbative approximation to full
current-density-functional theory is implemented for the first time, and found
to be numerically feasible. Different parametrizations for the
current-dependence of the density functional are critically compared. Orbital
currents in open-shell atoms turn out to produce a small shift in the
ionization energies. We find that modern density functionals have reached an
accuracy at which small current-related terms appearing in open-shell
configurations are not negligible anymore compared to the remaining difference
to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.
Tightened Lieb-Oxford bound for systems of fixed particle number
The Lieb-Oxford bound is a constraint upon approximate exchange-correlation
functionals. We explore a non-empirical tightening of that bound in both
universal and electron-number-dependent form. The test functional is PBE.
Regarding both atomization energies (slightly worsened) and bond lengths
(slightly bettered), we find the PBE functional to be remarkably insensitive to
the value of the Lieb-Oxford bound. This both rationalizes the use of the
original Lieb-Oxford constant in PBE and suggests that enhancement factors more
sensitive to sharpened constraints await discovery.Comment: six figures (color
Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study
We present a theoretical study on the response properties to an external
electric field of strongly correlated one-dimensional metals. Our investigation
is based on the recently developed Bethe-Ansatz local density approximation
(BALDA) to the density functional theory formulation of the Hubbard model. This
is capable of describing both Luttinger liquid and Mott-insulator correlations.
The BALDA calculated values for the static linear polarizability are compared
with those obtained by numerically accurate methods, such as exact (Lanczos)
diagonalization and the density matrix renormalization group, over a broad
range of parameters. In general BALDA linear polarizabilities are in good
agreement with the exact results. The response of the exact exchange and
correlation potential is found to point in the same direction of the perturbing
potential. This is well reproduced by the BALDA approach, although the fine
details depend on the specific parameterization for the local approximation.
Finally we provide a numerical proof for the non-locality of the exact exchange
and correlation functional.Comment: 8 pages and 8 figure
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.
Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
Bounds on the exchange-correlation energy of many-electron systems are
derived and tested. By using universal scaling properties of the
electron-electron interaction, we obtain the exponent of the bounds in three,
two, one, and quasi-one dimensions. From the properties of the electron gas in
the dilute regime, the tightest estimate to date is given for the numerical
prefactor of the bound, which is crucial in practical applications. Numerical
tests on various low-dimensional systems are in line with the bounds obtained,
and give evidence of an interesting dimensional crossover between two and one
dimensions
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.
Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
We present an extensive numerical study of ground-state properties of
confined repulsively interacting fermions on one-dimensional optical lattices.
Detailed predictions for the atom-density profiles are obtained from parallel
Kohn-Sham density-functional calculations and quantum Monte Carlo simulations.
The density-functional calculations employ a Bethe-Ansatz-based local-density
approximation for the correlation energy, which accounts for Luttinger-liquid
and Mott-insulator physics. Semi-analytical and fully numerical formulations of
this approximation are compared with each other and with a cruder
Thomas-Fermi-like local-density approximation for the total energy. Precise
quantum Monte Carlo simulations are used to assess the reliability of the
various local-density approximations, and in conjunction with these allow to
obtain a detailed microscopic picture of the consequences of the interplay
between particle-particle interactions and confinement in one-dimensional
systems of strongly correlated fermions.Comment: 14 pages, 11 figures, 1 table, submitte
- …