Solving the Kadanoff-Baym Equations for Inhomogeneous Systems: Application to Atoms and Molecules

Dahlen, Nils Erik; Leeuwen, Robert van

doi:10.1103/physrevlett.98.153004

Cited by 140 publications

(187 citation statements)

References 22 publications

(26 reference statements)

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“…(17) requires a transformation into equations for real times, known as KB equations, which are then solved by time propagation. 16,20,21,52 From the knowledge of the Green's function any one-particle property of the system can be extracted. In particular, the time-dependent density can be obtained from the lesser Green's function as…”

Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

“…[15][16][17][18][19] In the MBPT, the many-body self-energy MB can be approximated by a selection of suitable Feynman diagrams, relevant for the description of the main scattering processes. In earlier work 31 we have found that the 2B approximation is in excellent agreement with accurate TD-DMRG results in the regime of weak to intermediate interaction strength for the Anderson impurity model.…”

Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

“…13,14 In the context of time-dependent (TD) DFT, the inclusion of memory effects beyond the adiabatic approximation is not straightforward and the development of accurate functionals to be used in numerical calculations is still under way. A promising and timely, even though computationally demanding, alternative is the solution of the Kadanoff-Baym (KB) equations [15][16][17][18][19][20][21] using self-energies from many-body perturbation theory (MBPT). The advantage of MBPT over TDDFT is the inclusion of dynamical exchangecorrelation (XC) effects, i.e., effects arising from a frequencydependent self-energy, in a more systematic way through the selection of suitable Feynman diagrams.…”

Section: Introductionmentioning

confidence: 99%

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Correlation effects in bistability at the nanoscale: Steady state and beyond

et al. 2012

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The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the nonequilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born, and GW level. Assuming the existence of a steady state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate whether and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.

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Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

Section: Many-body Technique: Kadanoff-baym Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Correlation effects in bistability at the nanoscale: Steady state and beyond

et al. 2012

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“…The nonequilibrium 2B has recently been applied to study atoms in laser fields. 44 On the contour, the 2B self-energy reads ͓with the effective interaction ͑30͔͒…”

Section: Nonequilibrium Second Born Approximationmentioning

confidence: 99%

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

2008

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We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the nonequilibrium Keldysh formalism. The scheme is general and can be used with any quasiparticle self-energy, but for practical reasons, we mainly specialize to the so-called GW self-energy, widely used to describe the quasiparticle band structures and spectroscopic properties of extended and lowdimensional systems. We restrict the GW self-energy to a finite, central region containing the molecule, and we describe the leads by density functional theory ͑DFT͒. A minimal basis of maximally localized Wannier functions is applied both in the central GW region and the leads. The importance of using a conserving, i.e., fully self-consistent, GW self-energy is demonstrated both analytically and numerically. We introduce an effective spin-dependent interaction which automatically reduces self-interaction errors to all orders in the interaction. The scheme is applied to the Anderson model in and out of equilibrium. In equilibrium at zero temperature, we find that GW describes the Kondo resonance fairly well for intermediate interaction strengths. Out of equilibrium, we demonstrate that the one-shot G 0 W 0 approximation can produce severe errors, in particular, at high bias. Finally, we consider a benzene molecule between featureless leads. It is found that the molecule's highest occupied molecular orbital-lowest unoccupied molecular orbital gap as calculated in GW is significantly reduced as the coupling to the leads is increased, reflecting the more efficient screening in the strongly coupled junction. For the I-V characteristics of the junction, we find that Hartree-Fock ͑HF͒ and G 0 W 0 ͓G HF ͔ yield results closer to GW than does DFT and G 0 W 0 ͓G DFT ͔. This is explained in terms of selfinteraction effects and lifetime reduction due to electron-electron interactions.

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“…It can also be used with many-body effects included through self-energy terms, in the Kadanoff-Baym/Keldysh equations for time-dependent and nonequilibrium problems. 37,38 The chief limitation is the use of localized basis functions and the approximation of Eq. ͑12͒.…”

Section: ͑50͒mentioning

confidence: 99%

Coupling of electrons to the electromagnetic field in a localized basis

Allen

2008

Phys. Rev. B

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A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in, e.g., first-principlesbased simulations of the coupled dynamics of electrons and nuclei in materials and molecules responding to ultrashort laser pulses. Some additional aspects of nonadiabatic dynamical simulations are also discussed, including the potential of "reduced Ehrenfest" simulations for treating problems where standard Ehrenfest simulations will fail. DOI: 10.1103/PhysRevB.78.064305 PACS number͑s͒: 78.20.Bh, 71.15.Pd It is now possible to perform first-principles simulations of the coupled dynamics of electrons and nuclei with all nuclear coordinates included 1-4 rather than a subset of nominal reaction coordinates. For very large systems or when many trajectories are necessary, it is convenient to use a first-principles-based scheme 5-8 with a valence-electron Hamiltonian and ion-ion repulsive potential derived from calculations using density functional or other first-principles techniques. Here we are mainly concerned with the issue of how one can efficiently and accurately couple electrons to the electromagnetic field in such an approach, where matrix elements of various operators between localized basis functions ͑or "atomic orbitals"͒ can be calculated from first principles, and then used in large-scale calculations for complex systems, such as materials and molecules, responding to applied fields, such as ultrashort laser pulses. [9][10][11][12][13][14][15][16][17][18][19] Our starting point is, of course, the time-dependent Schrödinger equation, iប ‫ץ‬ ‫ץ‬t ͑x,t͒ = Ĥ ͑x,t͒, ͑1͒Some time ago, Graf and Vogl 20 obtained a result, used in Refs. 13-19, which is the time-dependent version of the Peierls substitution: If H 0 is the Hamiltonian matrix in a localized basis with no applied field,and H is the approximate Hamiltonian when there is an applied field with vector potential A͑x , t͒, then they are related bywith A͑t͒ = ͓A͑XЈ,t͒ + A͑X,t͔͒/2. ͑5͒Here ᐉ labels a localized basis function centered on a nucleus whose instantaneous position is X͑ᐉ , t͒, and we adopt the convention of normally suppressing the indices ᐉ and ᐉЈ as well as the time t by just writing X and XЈ. We will ignore any applied scalar potential A 0 , any B · B spin interactions, and the coupling of ion cores or nuclei to the applied fields since these effects can be easily included when necessary.With the prescription of Eq. ͑4͒, one does not need any new parameters in a calculation that employs either a semiempirical 13,14 or a first-principles-based [15][16][17][18][19] Hamiltonian H 0 whose elements are known as a function of ͑X − XЈ͒. On the other hand, this prescription is in one respect a rather crude approximation: It omits intra-atomic excitations and would therefore give no excitation at all for isolated atoms.Here a more general version of the result of Ref. 20 will be obtained in a form that is almost equally convenient for...

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Solving the Kadanoff-Baym Equations for Inhomogeneous Systems: Application to Atoms and Molecules

Cited by 140 publications

References 22 publications

Correlation effects in bistability at the nanoscale: Steady state and beyond

Correlation effects in bistability at the nanoscale: Steady state and beyond

ConservingGWscheme for nonequilibrium quantum transport in molecular contacts

Coupling of electrons to the electromagnetic field in a localized basis

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