512 research outputs found
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
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
The generator coordinate method in time-dependent density-functional theory: memory made simple
The generator coordinate (GC) method is a variational approach to the quantum
many-body problem in which interacting many-body wave functions are constructed
as superpositions of (generally nonorthogonal) eigenstates of auxiliary
Hamiltonians containing a deformation parameter. This paper presents a
time-dependent extension of the GC method as a new approach to improve existing
approximations of the exchange-correlation (XC) potential in time-dependent
density-functional theory (TDDFT). The time-dependent GC method is shown to be
a conceptually and computationally simple tool to build memory effects into any
existing adiabatic XC potential. As an illustration, the method is applied to
driven parametric oscillations of two interacting electrons in a harmonic
potential (Hooke's atom). It is demonstrated that a proper choice of
time-dependent generator coordinates in conjunction with the adiabatic
local-density approximation reproduces the exact linear and nonlinear
two-electron dynamics quite accurately, including features associated with
double excitations that cannot be captured by TDDFT in the adiabatic
approximation.Comment: 10 pages, 13 figure
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.
Andreev reflection and Klein tunneling in graphene
This is a colloquium-style introduction to two electronic processes in a
carbon monolayer (graphene), each having an analogue in relativistic quantum
mechanics. Both processes couple electron-like and hole-like states, through
the action of either a superconducting pair potential or an electrostatic
potential. The first process, Andreev reflection, is the electron-to-hole
conversion at the interface with a superconductor. The second process, Klein
tunneling, is the tunneling through a p-n junction. Existing and proposed
experiments on Josephson junctions and bipolar junctions in graphene are
discussed from a unified perspective.
CONTENTS:
I. INTRODUCTION
II. BASIC PHYSICS OF GRAPHENE (Dirac equation; Time reversal symmetry;
Boundary conditions; Pseudo-diffusive dynamics)
III. ANDREEV REFLECTION (Electron-hole conversion; Retro-reflection vs.
specular reflection; Dirac-Bogoliubov-de Gennes equation; Josephson junctions;
Further reading)
IV. KLEIN TUNNELING (Absence of backscattering; Bipolar junctions; Magnetic
field effects; Further reading)
V. ANALOGIES (Mapping between NS and p-n junction; Retro-reflection vs.
negative refraction; Valley-isospin dependent quantum Hall effect;
Pseudo-superconductivity)Comment: 20 pages, 28 figures; "Colloquium" for Reviews of Modern Physic
Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field
We derive a closed analytical expression for the exchange energy of the
three-dimensional interacting electron gas in strong magnetic fields, which
goes beyond the quantum limit (L=0) by explicitly including the effect of the
second, L=1, Landau level and arbitrary spin polarization. The inclusion of the
L=1 level brings the fields to which the formula applies closer to the
laboratory range, as compared to previous expressions, valid only for L=0 and
complete spin polarization. We identify, and explain, two distinct regimes,
separated by a critical density . Below , the per-particle exchange
energy is lowered by the contribution of L=1, whereas above it is
increased. As special cases of our general equation we recover various known,
more limited, results for higher fields, and identify and correct a few
inconsistencies in some of these earlier expressions.Comment: 7 pages, 2 figures, PRB accepte
Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals
The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of
quantum mechanics, and constitutes the basis for the very successful
density-functional approach to inhomogeneous interacting many-particle systems.
Here we show that in formulations of density-functional theory (DFT) that
employ more than one density variable, applied to systems with a degenerate
ground state, there is a subtle loophole in the HK theorem, as all mappings
between densities, wave functions and potentials can break down. Two weaker
theorems which we prove here, the joint-degeneracy theorem and the
internal-energy theorem, restore the internal, total and exchange-correlation
energy functionals to the extent needed in applications of DFT to atomic,
molecular and solid-state physics and quantum chemistry. The joint-degeneracy
theorem constrains the nature of possible degeneracies in general many-body
systems
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
Nonuniqueness of the Potentials of Spin-Density-Functional Theory
It is shown that, contrary to widely held beliefs, the potentials of
spin-density-functional theory (SDFT) are not unique functionals of the spin
densities. Explicit examples of distinct sets of potentials with the same
ground-state densities are constructed, and general arguments that uniqueness
should not occur in SDFT and other generalized density-functional theories are
given. As a consequence, various types of applications of SDFT require
significant corrections or modifications.Comment: 4 pages, no figure
Universal and nonuniversal contributions to block-block entanglement in many-fermion systems
We calculate the entanglement entropy of blocks of size x embedded in a
larger system of size L, by means of a combination of analytical and numerical
techniques. The complete entanglement entropy in this case is a sum of three
terms. One is a universal x and L-dependent term, first predicted by Calabrese
and Cardy, the second is a nonuniversal term arising from the thermodynamic
limit, and the third is a finite size correction. We give an explicit
expression for the second, nonuniversal, term for the one-dimensional Hubbard
model, and numerically assess the importance of all three contributions by
comparing to the entropy obtained from fully numerical diagonalization of the
many-body Hamiltonian. We find that finite-size corrections are very small. The
universal Calabrese-Cardy term is equally small for small blocks, but becomes
larger for x>1. In all investigated situations, however, the by far dominating
contribution is the nonuniversal term steming from the thermodynamic limit.Comment: 6 pages, 3 figure
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