3,947 research outputs found
U(1)SU(2) Gauge Invariance Made Simple for Density Functional Approximations
A semi-relativistic density-functional theory that includes spin-orbit
couplings and Zeeman fields on equal footing with the electromagnetic
potentials, is an appealing framework to develop a unified first-principles
computational approach for non-collinear magnetism, spintronics, orbitronics,
and topological states. The basic variables of this theory include the
paramagnetic current and the spin-current density, besides the particle and the
spin density, and the corresponding exchange-correlation (xc) energy functional
is invariant under local U(1)SU(2) gauge transformations. The xc-energy
functional must be approximated to enable practical applications, but, contrary
to the case of the standard density functional theory, finding simple
approximations suited to deal with realistic atomistic inhomogeneities has been
a long-standing challenge. Here, we propose a way out of this impasse by
showing that approximate gauge-invariant functionals can be easily generated
from existing approximate functionals of ordinary density-functional theory by
applying a simple {\it minimal substitution} on the kinetic energy density,
which controls the short-range behavior of the exchange hole. Our proposal
opens the way to the construction of approximate, yet non-empirical
functionals, which do not assume weak inhomogeneity and should therefore have a
wide range of applicability in atomic, molecular and condensed matter physics
Functional theories of thermoelectric phenomena
We review the progress that has been recently made in the application of
time-dependent density functional theory to thermoelectric phenomena. As the
field is very young, we emphasize open problems and fundamental issues. We
begin by introducing the formal structure of \emph{thermal density functional
theory}, a density functional theory with two basic variables -- the density
and the energy density -- and two conjugate fields -- the ordinary scalar
potential and Luttinger's thermomechanical potential. The static version of
this theory is contrasted with the familiar finite-temperature density
functional theory, in which only the density is a variable. We then proceed to
constructing the full time-dependent non equilibrium theory, including the
practically important Kohn-Sham equations that go with it. The theory is shown
to recover standard results of the Landauer theory for thermal transport in the
steady state, while showing greater flexibility by allowing a description of
fast thermal response, temperature oscillations and related phenomena. Several
results are presented here for the first time, i.e., the proof of invertibility
of the thermal response function in the linear regime, the full expression of
the thermal currents in the presence of Luttinger's thermomechanical potential,
an explicit prescription for the evaluation of the Kohn-Sham potentials in the
adiabatic local density approximation, a detailed discussion of the leading
dissipative corrections to the adiabatic local density approximation and the
thermal corrections to the resistivity that follow from it.Comment: 34 pages, 6 figure
On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory
Physically valid and numerically efficient approximations for the exchange
and correlation energy are critical for reduced density-matrix functional
theory to become a widely used method in electronic structure calculations.
Here we examine the physical limits of power functionals of the form
for the scaling function in the exchange-correlation
energy. To this end we obtain numerically the minimizing momentum distributions
for the three- and two-dimensional homogeneous electron gas, respectively. In
particular, we examine the limiting values for the power to yield
physically sound solutions that satisfy the Lieb-Oxford lower bound for the
exchange-correlation energy and exclude pinned states with the condition
for all wave vectors . The results refine the
constraints previously obtained from trial momentum distributions. We also
compute the values for that yield the exact correlation energy and its
kinetic part for both the three- and two-dimensional electron gas. In both
systems, narrow regimes of validity and accuracy are found at and at for the density parameter, corresponding to
relatively low densities.Comment: Phys. Rev. A (in print, 2016
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