274 research outputs found
First-principles approach to excitons in time-resolved and angle-resolved photoemission spectra
We show that any {\em quasi-particle} or GW approximation to the self-energy
does not capture excitonic features in time-resolved (TR) photoemission
spectroscopy. In this work we put forward a first-principles approach and
propose a feasible diagrammatic approximation to solve this problem. We also
derive an alternative formula for the TR photocurrent which involves a single
time-integral of the lesser Green's function. The diagrammatic approximation
applies to the {\em relaxed} regime characterized by the presence of
quasi-stationary excitons and vanishing polarization. The main distinctive
feature of the theory is that the diagrams must be evaluated using {\em
excited} Green's functions. As this is not standard the analytic derivation is
presented in detail. The final result is an expression for the lesser Green's
function in terms of quantities that can all be calculated {\em ab initio}. The
validity of the proposed theory is illustrated in a one-dimensional model
system with a direct gap. We discuss possible scenarios and highlight some
universal features of the exciton peaks. Our results indicate that the exciton
dispersion can be observed in TR {\em and} angle-resolved photoemission.Comment: 15 pages, 8 figure
Non-equilibrium Bethe-Salpeter equation for transient photo-absorption spectroscopy
In this work we propose an accurate first-principle approach to calculate the
transient photo--absorption spectrum measured in Pump\&\,Probe experiments. We
formulate a condition of {\em adiabaticity} and thoroughly analyze the
simplifications brought about by the fulfillment of this condition in the
non--equilibrium Green's function (NEGF) framework. Starting from the
Kadanoff-Baym equations we derive a non--equilibrium Bethe--Salpeter equation
(BSE) for the response function that can be implemented in most of the already
existing {\em ab--initio} codes. In addition, the {\em adiabatic} approximation
is benchmarked against full NEGF simulations in simple model hamiltonians, even
under extreme, nonadiabatic conditions where it is expected to fail. We find
that the non--equilibrium BSE is very robust and captures important spectral
features in a wide range of experimental configurations.Comment: 13 pages, 5 captioned figure
Benchmarking Nonequilibrium Green's Functions against Configuration Interaction for time-dependent Auger decay processes
We have recently proposed a Nonequilibrium Green's Function (NEGF) approach
to include Auger decay processes in the ultrafast charge dynamics of
photoionized molecules. Within the so called Generalized Kadanoff-Baym Ansatz
the fundamental unknowns of the NEGF equations are the reduced one-particle
density matrix of bound electrons and the occupations of the continuum states.
Both unknowns are one-time functions like the density in Time-Dependent
Functional Theory (TDDFT). In this work we assess the accuracy of the approach
against Configuration Interaction (CI) calculations in one-dimensional model
systems. Our results show that NEGF correctly captures qualitative and
quantitative features of the relaxation dynamics provided that the energy of
the Auger electron is much larger than the Coulomb repulsion between two holes
in the valence shells. For the accuracy of the results dynamical
electron-electron correlations or, equivalently, memory effects play a pivotal
role. The combination of our NEGF approach with the Sham-Schl\"uter equation
may provide useful insights for the development of TDDFT exchange-correlation
potentials with a history dependence.Comment: 7 pages, 3 figure
Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects
We study time-dependent quantum transport in a correlated model system by
means of time-propagation of the Kadanoff-Baym equations for the nonequilibrium
many-body Green function. We consider an initially contacted equilibrium system
of a correlated central region coupled to tight-binding leads. Subsequently a
time-dependent bias is switched on after which we follow in detail the
time-evolution of the system. Important features of the Kadanoff-Baym approach
are 1) the possibility of studying the ultrafast dynamics of transients and
other time-dependent regimes and 2) the inclusion of exchange and correlation
effects in a conserving approximation scheme. We find that initial correlation
and memory terms due to many-body interactions have a large effect on the
transient currents. Furthermore the value of the steady state current is found
to be strongly dependent on the approximation used to treat the electronic
interactions.Comment: 5 pages, 2 figure
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
Ultra-nonlocality in density functional theory for photo-emission spectroscopy
We derive an exact expression for the photo-current of photo-emission
spectroscopy using time-dependent current density functional theory (TDCDFT).
This expression is given as an integral over the Kohn-Sham spectral function
renormalized by effective potentials that depend on the exchange-correlation
kernel of current density functional theory. We analyze in detail the physical
content of this expression by making a connection between the
density-functional expression and the diagrammatic expansion of the
photo-current within many-body perturbation theory. We further demonstrate that
the density functional expression does not provide us with information on the
kinetic energy distribution of the photo-electrons. Such information can, in
principle, be obtained from TDCDFT by exactly modeling the experiment in which
the photo-current is split into energy contributions by means of an external
electromagnetic field outside the sample, as is done in standard detectors. We
find, however, that this procedure produces very nonlocal correlations between
the exchange-correlation fields in the sample and the detector.Comment: 11 pages, 11 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
First-principles nonequilibrium Green's function approach to transient photoabsorption: Application to atoms
We put forward a first-principle NonEquilibrium Green's Function (NEGF)
approach to calculate the transient photoabsorption spectrum of optically thin
samples. The method can deal with pump fields of arbitrary strength, frequency
and duration as well as for overlapping and nonoverlapping pump and probe
pulses. The electron-electron repulsion is accounted for by the correlation
self-energy, and the resulting numerical scheme deals with matrices that scale
quadratically with the system size. Two recent experiments, the first on helium
and the second on krypton, are addressed. For the first experiment we explain
the bending of the Autler-Townes absorption peaks with increasing the
pump-probe delay \t, and relate the bending to the thickness and density of
the gas. For the second experiment we find that sizable spectral structures of
the pump-generated admixture of Kr ions are fingerprints of {\em dynamical
correlation} effects, and hence they cannot be reproduced by time-local
self-energy approximations. Remarkably, the NEGF approach also captures the
retardation of the absorption onset of Kr with respect to Kr as a
function of \t.Comment: 13 pages, 8 captioned figure
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
On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches
We present a comprehensive analysis of the relaxation dynamics of a Luttinger
liquid subject to a sequence of sudden interaction quenches. We express the
critical exponent governing the decay of the steady-state propagator as
an explicit functional of the switching protocol. At long distances
depends only on the initial state while at short distances it is also history
dependent. Continuous protocols of arbitrary complexity can be realized with
infinitely long sequences. For quenches of finite duration we prove that there
exist no protocol to bring the initial non-interacting system in the ground
state of the Luttinger liquid. Nevertheless memory effects are washed out at
short-distances. The adiabatic theorem is then investigated with
ramp-switchings of increasing duration, and several analytic results for both
the propagator and the excitation energy are derived.Comment: 7 pages, 4 figure
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