Non-equilibrium Green’s Functions for Coupled Fermion-Boson Systems

Karlsson, Daniel; Leeuwen, Robert van

doi:10.1007/978-3-319-42913-7_8-1

Cited by 8 publications

(11 citation statements)

References 38 publications

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“…These non-equilibrium Green's functions obey the Kadanoff-Baym and not Hedin's equations. The Keldysh contour formalism goes beyond the scope of this review article and we refer the interested reader to two excellent recent books (Stefanucci and Leeuwen, 2013; Karlsson and Leeuwen, 2018).…”

Section: Current Challenges and Beyond Gwmentioning

confidence: 99%

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

2019

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The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW , a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

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Section: Current Challenges and Beyond Gwmentioning

confidence: 99%

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

2019

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“…and D > μν ðt;t 0 Þ ¼ D < νμ ðt 0 ;tÞ. The expectation value of Δφ H;μ ðtÞ is identically zero by construction, a property which simplifies the bosonic KBE [22,47]:…”

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confidence: 99%

“…The numerical solution of the coupled Eqs. ( 4) and ( 7) is demanding (cubic scaling with the number of time steps) and so far achieved only in small model systems [22,24,47,48]. In this work, we consider the GD approximation shown diagrammatically in Fig.…”

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confidence: 99%

Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics

et al. 2021

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The interaction of electrons with quantized phonons and photons underlies the ultrafast dynamics of systems ranging from molecules to solids, and it gives rise to a plethora of physical phenomena experimentally accessible using time-resolved techniques. Green's function methods offer an invaluable interpretation tool since scattering mechanisms of growing complexity can be selectively incorporated in the theory. Currently, however, real-time Green's function simulations are either prohibitively expensive due to the cubic scaling with the propagation time or do neglect the feedback of electrons on the bosons, thus violating energy conservation. We put forward a computationally efficient Green's function scheme which overcomes both limitations. The numerical effort scales linearly with the propagation time while the simultaneous dressing of electrons and bosons guarantees the fulfillment of all fundamental conservation laws. We present a real-time study of the phonon-driven relaxation dynamics in an optically excited narrow band-gap insulator, highlighting the nonthermal behavior of the phononic degrees of freedom. Our formulation paves the way to first-principles simulations of electron-boson systems with unprecedented long propagation times.

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“…It is therefore difficult to avoid double counting electronic interactions, and the many-body formalisms that have been proposed 35,67,76,87 are still more complicated than the widely-used BObased approach outlined above, although work in this direction is ongoing. 79,84,88 To avoid double-counting issues, it would be desirable to be able to calculate electronic and phononic observables within a formally-exact DFT-like framework. This is possible in multicomponent DFT, 89 where the functionals depend on both the electronic density n(r) in the body-fixed frame and the N n -body nuclear density Γ(R 1 , R 2 , .…”

Section: Introductionmentioning

confidence: 99%

Exact factorization-based density functional theory of electron-phonon systems

2019

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Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density nU (r), a conditional probability density depending parametrically on the phonon normal mode amplitudes U = {U qλ }, is coupled to the nuclear Schrödinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrödinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the nonadiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phononinduced band structure renormalization in the Fröhlich model.

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Non-equilibrium Green’s Functions for Coupled Fermion-Boson Systems

Cited by 8 publications

References 38 publications

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics

Exact factorization-based density functional theory of electron-phonon systems

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