Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems
In this thesis, an approximate method introduced to solve time-dependent many-body problems known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations, are introduced. In practice, the associated integral kernels known as the electron Σ and phonon self-energies 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. Time-dependent systems of interest are studied in this thesis by using the integro-diﬀerential forms of the Dyson equations referred to as the Kadanoﬀ-Baym Equations (KBE). The Kadanoﬀ-Baym equations are introduced for the electron and phonon propagators unconventionally as coupled ﬁrstorder integro-diﬀerential 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 Kadanoﬀ-Baym equations allow to solve the Bethe-Salpeter 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 self-consistent Born approximations against numerically exact results for the two- site, two-electron Holstein model. In this model, the two electrons which are constrained to move between two lattice sites interact indirectly via the electron-phonon coupling. It was observed that only the fully self-consistent 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 self-consistent Born approximation was concluded to fail in describing the bipolaronic behavior of the true system. In the third publication, we benchmarked the Hartree-Fock and second Born approximations against an exact method for the few-site Hubbard and Pariser-Parr-Pople 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 so-called correlation induced doubly-excited states. This is not possible for time-local approximations such as Hartree-Fock. In addition to the qualitative results, which highlight successes of the applied simple self-energy 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 many-body approximations used, with the aim to better understand when these methods are predictive. ...
PublisherUniversity of Jyväskylä
monen kappaleen teoria aikariippuva monihiukkashäiriöteoria Greenin funktio many-body problems many-body theory time-dependent many-body perturbation theory Green's function electron-phonon interaction excitation spectra kiinteän olomuodon fysiikka kvanttimekaniikka numeeriset menetelmät approksimointi elektronit fononit spektroskopia
MetadataShow full item record
- Väitöskirjat 
Showing items with similar title or keywords.
Myöhänen, Petri (University of Jyväskylä, 2012)During the recent decades, molecular electronics has established its place as one of the promising fields in the nanoscience. The possibility to manufacture and control molecular junctions where single molecules are ...
Developments in many-body theory of quantum transport and spectroscopy with non-equilibrium Green's functions and time-dependent density functional theory Uimonen, Anna-Maija (University of Jyväskylä, 2015)The problem of quantum dynamics in open systems has gained attention in recent decades and not the least due to the advances made in quantum transport in molecular systems. The main motivation behind quantum transport ...
Ojajärvi, Risto (2017)Parhaiten tunnettu suprajohtavuuden syntymekanismi perustuu fononien välittämään vetovoimaan elektronien välillä. Tässä tutkielmassa tutkin fononien välittämää suprajohtavuutta systeemeissä, jossa elektronivyöt ovat ...
Cort Barrada, Luis; Karlsson, Daniel; Lani, Giovanna; van Leeuwen, Robert (American Physical Society, 2017)We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as ...
Acoustic wave tunneling across a vacuum gap between two piezoelectric crystals with arbitrary symmetry and orientation Geng, Zhuoran; Maasilta, Ilari J. (American Physical Society (APS), 2022)It is not widely appreciated that an acoustic wave can “jump” or “tunnel” across a vacuum gap between two piezoelectric solids, nor has the general case been formulated or studied in detail. Here, we remedy that situation, ...