The Kadanoff–Baym approach to double excitations in finite systems

Säkkinen, Niko; Manninen, M.; Leeuwen, Robert van

doi:10.1088/1367-2630/14/1/013032

Cited by 37 publications

(51 citation statements)

References 32 publications

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“…To answer we have to find the diagrammatic structure encoded in the kernel of the BSE. where L 0 (12; 34) = G(1, 4)G(2, 3) and the fourpoint reducible kernel K is given by K(12; 34) = −iδΣ(1, 3)/δG (4,2). The variation of the Green's function is related to the two-particle Green's function and therefore L is related to the two-particle excitation spectrum.…”

Section: Examplesmentioning

confidence: 99%

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

et al. 2015

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In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the selfenergy 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 on the left-half of the diagram, antitime-ordered Green's functions on the right-half of the diagram and lesser or greater Green's function 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 Green's functions and subsequently extend it to dressed Green's functions. 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.

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Section: Examplesmentioning

confidence: 99%

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

et al. 2015

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“…with |X being the eigenstates ofĤ 2 (having energy E X ) and c X = X|gs denoting the expansion coefficients with respect to the ground state |gs ofĤ 0 . In contrast to the HF approximation, a second-order self-energy (as 2B) has the ability to describe double excitations, see [22]. For this reason, the 2B+GKBA calculations capture the transition ω AD and, accordingly, also ω CD .…”

Section: Discussionmentioning

confidence: 99%

The generalized Kadanoff-Baym ansatz. Computing nonlinear response properties of finite systems

Balzer

Hermanns

Bönitz

2013

J. Phys.: Conf. Ser.

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For a minimal Hubbard-type system at different interaction strengths U , we investigate the density-response for an excitation beyond the linear regime using the generalized Kadanoff-Baym ansatz (GKBA) and the second Born (2B) approximation. We find strong correlation features in the response spectra and establish the connection to an involved double excitation process. By comparing approximate and exact Green's function results, we also observe an anomalous U -dependence of the energy of this double excitation in 2B+GKBA. This is in accordance with earlier findings [K. Balzer et al., EPL 98, 67002 (2012)] on double excitations in quantum wells.

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“…We mention that the 2B approximation has been successfully applied to equilibrium spectral properties [49] and total energies [50] of molecular systems. Comparisons against numerically accurate real-time simulations of 1D systems [18,51] and weakly correlated model nanostructures of different geometries [29,30,39,[52][53][54][55][56] indicate that the 2B approximation remains accurate even out of equilibrium. The last term I Auger can be written as in Eq.…”

Section: A Negf Equationsmentioning

confidence: 99%

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

Perfetto

Stefanucci

2018

J. Phys.: Condens. Matter

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We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed. arXiv:1810.03322v1 [cond-mat.other]

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The Kadanoff–Baym approach to double excitations in finite systems

Cited by 37 publications

References 32 publications

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

The generalized Kadanoff-Baym ansatz. Computing nonlinear response properties of finite systems

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

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