Application of timedependent manybody perturbation theory to excitation spectra of selected finite model systems
In this thesis, an approximate method introduced to solve timedependent manybody problems
known as timedependent manybody perturbation theory is studied. Manybody perturbation theory
for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an
unconventional twocomponent phonon propagator, which satisfy coupled integral Dyson equations,
are introduced. In practice, the associated integral kernels known as the electron Σ and phonon
selfenergies need to be approximated. The conserving approximations known as the Hartree (Fock)
and the ﬁrst and second Born approximations, which respect the continuity equation between the
electron density and current, are considered in this work.
Timedependent systems of interest are studied in this thesis by using the integrodiﬀerential forms
of the Dyson equations referred to as the KadanoﬀBaym Equations (KBE). The KadanoﬀBaym
equations are introduced for the electron and phonon propagators unconventionally as coupled ﬁrstorder integrodiﬀerential equations. It is reviewed how these equations are solved numerically by
describing an integration rule, a class of practical methods and a parallel implementation of the
numerical method. In addition, documentation of how the KadanoﬀBaym equations allow to solve
the BetheSalpeter Equation (BSE) with the kernel δΣ/δG for the density response function, is
provided.
In two of the enclosed publications, we benchmarked observables obtained by using the Hartree and
partially and fully selfconsistent Born approximations against numerically exact results for the two
site, twoelectron Holstein model. In this model, the two electrons which are constrained to move
between two lattice sites interact indirectly via the electronphonon coupling. It was observed that
only the fully selfconsistent Born approximation could cope qualitatively correctly with the competition between the delocalizing and localizing eﬀects of the kinetic and interaction energies. For the
other two approximations, spurious bifurcative symmetry breaking with an associated unbounded
density response was observed. Nevertheless, also the selfconsistent Born approximation was concluded to fail in describing the bipolaronic behavior of the true system. In the third publication,
we benchmarked the HartreeFock and second Born approximations against an exact method for
the fewsite Hubbard and PariserParrPople models in which the underlying lattice is inert and the
electrons interact amongst themselves directly. It was found that the second Born approximation is
capable of describing the socalled correlation induced doublyexcited states. This is not possible for
timelocal approximations such as HartreeFock.
In addition to the qualitative results, which highlight successes of the applied simple selfenergy approximations, the approximate and exact results were also compared on a more quantitative level. It
is the quantitative and qualitative results combined which are used in this thesis to assess the quality
of the manybody approximations used, with the aim to better understand when these methods are
predictive.
...
Publisher
University of JyväskyläISBN
9789513968144ISSN Search the Publication Forum
0075465XKeywords
monen kappaleen teoria aikariippuva monihiukkashäiriöteoria Greenin funktio manybody problems manybody theory timedependent manybody perturbation theory Green's function electronphonon interaction excitation spectra kiinteän olomuodon fysiikka kvanttimekaniikka numeeriset menetelmät approksimointi elektronit fononit spektroskopia
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