2,129 research outputs found
Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
We consider a general class of approximations which guarantees the
conservation of particle number in many-body perturbation theory. To do this we
extend the concept of -derivability for the self-energy to a
larger class of diagrammatic terms in which only some of the Green's function
lines contain the fully dressed Green's function . We call the corresponding
approximations for partially -derivable. A special subclass of
such approximations, which are gauge-invariant, is obtained by dressing loops
in the diagrammatic expansion of consistently with . These
approximations are number conserving but do not have to fulfill other
conservation laws, such as the conservation of energy and momentum. From our
formalism we can easily deduce if commonly used approximations will fulfill the
continuity equation, which implies particle number conservation. We further
show how the concept of partial -derivability plays an important role in
the derivation of a generalized sum rule for the particle number, which reduces
to the Luttinger-Ward theorem in the case of a homogeneous electron gas, and
the Friedel sum rule in the case of the Anderson model. To do this we need to
ensure that the Green's function has certain complex analytic properties, which
can be guaranteed if the spectral function is positive semi-definite.The latter
property can be ensured for a subset of partially -derivable
approximations for the self-energy, namely those that can be constructed from
squares of so-called half-diagrams. In case the analytic requirements are not
fulfilled we highlight a number of subtle issues related to branch cuts, pole
structure and multi-valuedness. We also show that various schemes of computing
the particle number are consistent for particle number conserving
approximations.Comment: Minor changes, corrected typo
Development of non-equilibrium Green's functions for use with full interaction in complex systems
We present an ongoing development of an existing code for calculating
ground-state, steady-state, and transient properties of many-particle systems.
The development involves the addition of the full four-index two electron
integrals, which allows for the calculation of transport systems, as well as
the extension to multi-level electronic systems, such as atomic and molecular
systems and other applications. The necessary derivations are shown, along with
some preliminary results and a summary of future plans for the code
Solving the Kadanoff-Baym equations for inhomogenous systems: Application to atoms and molecules
We have implemented time-propagation of the non-equilibrium Green function
for atoms and molecules, by solving the Kadanoff-Baym equations within a
conserving self-energy approximation. We here demonstrate the usefulnes of
time-propagation for calculating spectral functions and for describing the
correlated electron dynamics in a non-perturbative electric field. We also
demonstrate the use of time-propagation as a method for calculating
charge-neutral excitation energies, equivalent to highly advanced solutions of
the Bethe-Salpeter equation.Comment: 4 pages, 5 figure
Contour calculus for many-particle functions
In non-equilibrium many-body perturbation theory, Langreth rules are an
efficient way to extract real-time equations from contour ones. However, the
standard rules are not applicable in cases that do not reduce to simple
convolutions and multiplications. We introduce a procedure for extracting
real-time equations from general multi-argument contour functions with an
arbitrary number of arguments. This is done for both the standard Keldysh
contour, as well as the extended contour with a vertical track that allows for
general initial states. This amounts to the generalization of the standard
Langreth rules to much more general situations. These rules involve
multi-argument retarded functions as key ingredients, for which we derive
intuitive graphical rules. We apply our diagrammatic recipe to derive Langreth
rules for the so-called double triangle structure and the general vertex
function, relevant for the study of vertex corrections beyond the
approximation
Nonequilibrium green functions in time-dependent current-density-functional theory
We give an overview of the underlying concepts of time-dependent current-density functional theory (TDCDFT). We show how the basic equations of TDCDFT can be elegantly derived using the time contour method of nonequilibrium Green function theory. We further demonstrate how the formalism can be used to derive explicit equations for the exchange-correlation vector potentials and integral kernels for the Kohn-Sham equations and their linearized form.</p
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