62 research outputs found
Superatom molecular orbitals: a new type of long-lived electronic states
We present ab initio calculations of the quasiparticle decay times in a
Buckminsterfullerene based on the many-body perturbation theory. A particularly
lucid representation arises when the broadening of the quasiparticle states is
plotted in the angular momentum and energy coordinates. In this representation
the main spectroscopic features of the fullerene consist of two occupied nearly
parabolic bands, and delocalized plane-wave-like unoccupied states with a few
long-lived electronic states (the superatom molecular orbitals, SAMOs) embedded
in the continuum of Fermi-liquid states. SAMOs have been recently uncovered
experimentally by M. Feng, J. Zhao, and H. Petek [Science 320, 359 (2008)]
using scanning tunneling spectroscopy. The present calculations offer an
explanation of their unusual stability and unveil their long-lived nature
making them good candidates for applications in the molecular electronics. From
the fundamental point of view these states illustrate a concept of the
Fock-space localization [B. L. Altshuler, Y. Gefen, A. Kamenev, and L. S.
Levitov, Phys. Rev. Lett. 78, 2803 (1997)] with properties drastically
different from the Fermi-liquid excitations
Spectral properties from Matsubara Green’s function approach: Application to molecules
We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second- order treatment of the Coulomb interaction by benchmarking its accuracy for a well- established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equation
Vertex corrections for positive-definite spectral functions of simple metals
We present a systematic study of vertex corrections in the homogeneous
electron gas at metallic densities. The vertex diagrams are built using a
recently proposed positive-definite diagrammatic expansion for the spectral
function. The vertex function not only provides corrections to the well known
plasmon and particle-hole scatterings, but also gives rise to new physical
processes such as generation of two plasmon excitations or the decay of the
one-particle state into a two-particles-one-hole state. By an efficient Monte
Carlo momentum integration we are able to show that the additional scattering
channels are responsible for the bandwidth reduction observed in photoemission
experiments on bulk sodium, appearance of the secondary plasmon satellite below
the Fermi level, and a substantial redistribution of spectral weights. The
feasibility of the approach for first-principles band-structure calculations is
also discussed
Diagrammatic expansion for positive density-response spectra: Application to the electron gas
In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a
diagrammatic expansion for the self-energy which guarantees the positivity of
the spectral function. In this work we extend the theory to the density
response function. We write the generic diagram for the density-response
spectrum as the sum of partitions. In a partition the original diagram is
evaluated using time-ordered Green's functions (GF) on the left-half of the
diagram, antitime-ordered GF on the right-half of the diagram and lesser or
greater GF gluing the two halves. As there exist more than one way to cut a
diagram in two halves, to every diagram corresponds more than one partition. We
recognize that the most convenient diagrammatic objects for constructing a
theory of positive spectra are the half-diagrams. Diagrammatic approximations
obtained by summing the squares of half-diagrams do indeed correspond to a
combination of partitions which, by construction, yield a positive spectrum. We
develop the theory using bare GF and subsequently extend it to dressed GF. We
further prove a connection between the positivity of the spectral function and
the analytic properties of the polarizability. The general theory is
illustrated with several examples and then applied to solve the long-standing
problem of including vertex corrections without altering the positivity of the
spectrum. In fact already the first-order vertex diagram, relevant to the study
of gradient expansion, Friedel oscillations, etc., leads to spectra which are
negative in certain frequency domain. We find that the simplest approximation
to cure this deficiency is given by the sum of the zero-th order bubble
diagram, the first-order vertex diagram and a partition of the second-order
ladder diagram. We evaluate this approximation in the 3D homogeneous electron
gas and show the positivity of the spectrum for all frequencies and densities.Comment: 19 pages, 19 figure
Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
We present a diagrammatic approach to construct self-energy approximations
within many-body perturbation theory with positive spectral properties. The
method cures the problem of negative spectral functions which arises from a
straightforward inclusion of vertex diagrams beyond the GW approximation. Our
approach consists of a two-steps procedure: we first express the approximate
many-body self-energy as a product of half-diagrams and then identify the
minimal number of half-diagrams to add in order to form a perfect square. The
resulting self-energy is an unconventional sum of self-energy diagrams in which
the internal lines of half a diagram are time-ordered Green's functions whereas
those of the other half are anti-time-ordered Green's functions, and the lines
joining the two halves are either lesser or greater Green's functions. The
theory is developed using noninteracting Green's functions and subsequently
extended to self-consistent Green's functions. Issues related to the conserving
properties of diagrammatic approximations with positive spectral functions are
also addressed. As a major application of the formalism we derive the minimal
set of additional diagrams to make positive the spectral function of the GW
approximation with lowest-order vertex corrections and screened interactions.
The method is then applied to vertex corrections in the three-dimensional
homogeneous electron gas by using a combination of analytical frequency
integrations and numerical Monte-Carlo momentum integrations to evaluate the
diagrams.Comment: 19 pages, 19 figure
Time-linear quantum transport simulations with correlated nonequilibrium Green's functions
We present a time-linear scaling method to simulate open and correlated
quantum systems. The method inherits from many-body perturbation theory the
possibility to choose selectively the most relevant scattering processes in the
dynamics, thereby paving the way to the real-time characterization of
correlated ultrafast phenomena in quantum transport. The open system dynamics
is described in terms of an embedding correlator from which the time-dependent
current can be calculated using the Meir-Wingreen formula. We show how to
efficently implement the method through a simple grafting into recently
proposed time-linear Green's function schemes for closed systems.
Electron-electron and electron-phonon interactions can be treated on equal
footing while preserving all fundametal conservation laws.Comment: 6 pages, 3 figure
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