Extracting spectral properties from Keldysh Green functions

Dirks, Andreas; Eckstein, Martin; Pruschke, Thomas; Werner, Philipp

doi:10.1103/physreve.87.023305

Cited by 13 publications

(13 citation statements)

References 29 publications

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“…IV C, we also observe for N(ω, t) regions of negative spectral weight in certain time ranges, and particularly in the time range −1/Γ t +1/Γ where most of the spectral weight rearrangement takes place as a result of the shift of the satellite peaks from their initial to their final state positions. Such regions of negative spectral weight, for certain time ranges, are also observed in other systems 37,39,57 . Another feature of Fig.…”

Section: A Lesser Green Functionsupporting

confidence: 59%

Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy

2020

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We investigate several definitions of the time-dependent spectral function A(ω, t) of the Anderson impurity model following a quench and within the time-dependent numerical renormalization group (TDNRG) method. In terms of the single-particle two-time retarded Green function G r (t 1 , t 2 ), the definitions we consider differ in the choice of the time variable t with respect to t 1 and/or t 2 (which we refer to as the time reference). In a previous study [Nghiem et al. Phys. Rev. Lett. 119, 156601 (2017)], we investigated the spectral function A(ω, t), obtained from the Fourier transform of Im[G r (t 1 , t 2 )] w.r.t. the time difference t = t 1 − t 2 , with time reference t = t 2 . Here, we complement this work by deriving expressions for the retarded Green function for the choices t = t 1 and the average, or Wigner, time t = (t 1 + t 2 )/2, within the TDNRG approach. We compare and contrast the resulting A(ω, t) for the different choices of time reference. While the choice t = t 1 results in a spectral function with no time-dependence before the quench (t < 0) (being identical to the equilibrium initial-state spectral function for t < 0), the choices t = (t 1 + t 2 )/2 and t = t 2 exhibit nontrivial time evolution both before and after the quench. Expressions for the lesser, greater and advanced Green functions are also derived within TDNRG for all choices of time reference. The average time lesser Green function G < (ω, t) is particularly interesting, as it determines the time-dependent occupied density of states N(ω, t) = G < (ω, t)/(2πi), a quantity that determines the photoemission current in the context of time-resolved pump-probe photoemission spectroscopy. We present calculations for N(ω, t) for the Anderson model following a quench, and discuss the resulting time evolution of the spectral features, such as the Kondo resonance and high-energy satellite peaks. We also discuss the issue of thermalization at long times for N(ω, t). Finally, we use the results for N(ω, t) to calculate the time-resolved photoemission current for the Anderson model following a quench (acting as the pump) and study the different behaviors that can be observed for different resolution times of a Gaussian probe pulse.arXiv:1912.08474v2 [cond-mat.str-el] 10 Jan 2020 NRG which involve calculating expectation values of the form Ô 1 (t 1 )Ô 2 (t 2 ) ρ whereÔ 1 andÔ 2 are local operators, e.g., the operators d σ and d † σ in (1). C. Parameter quenchSince the main interest in this paper is to compare the timedependent spectral functions resulting from different choices of the time reference, we focus on a specific quench on the model (1). We consider switching from a symmetric Kondo regime with ε i = −15Γ, U i = 30Γ and a vanishingly small Kondo scale T i K = 3 × 10 −8 to a symmetric Kondo regime with ε f = −6Γ, U f = 12Γ and a larger Kondo scale T K = 2.5 × 10 −5 T i K = 0.0012T K , and a constant hybridization Γ ≡ πρ 0 (0)V 2 = 0.001. Thus, the quench is between two symmetric Kondo states with different degrees of correlation. D. Ti...

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Section: A Lesser Green Functionsupporting

confidence: 59%

Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy

2020

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“…3(a), is accompanied by small regions of negative spectral weight in this transient time range [73]. This does not violate any exact results for time-dependent, as opposed to steady-state, spectral functions, and is observed in other systems [30,80,81]. The spectral sum rule is satisfied analytically exactly at all times and numerically within 1% at all negative times and to higher accuracy at positive times for all quench protocols [73].…”

Section: Spectral Function A(ω T)-we Obtain the Time-dependent Specmentioning

confidence: 69%

Time Evolution of the Kondo Resonance in Response to a Quench

Nghiem

Costi

2017

Phys. Rev. Lett.

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We investigate the time evolution of the Kondo resonance in response to a quench by applying the timedependent numerical renormalization group (TDNRG) approach to the Anderson impurity model in the strong correlation limit. For this purpose, we derive within TDNRG a numerically tractable expression for the retarded two-time nonequilibrium Green function G(t + t , t), and its associated time-dependent spectral function, A(ω, t), for times t both before and after the quench. Quenches from both mixed valence and Kondo correlated initial states to Kondo correlated final states are considered. For both cases, we find that the Kondo resonance in the zero temperature spectral function, a preformed version of which is evident at very short times t → 0 + , only fully develops at very long times t 1/T K , where T K is the Kondo temperature of the final state. In contrast, the final state satellite peaks develop on a fast time scale 1/Γ during the time interval −1/Γ t +1/Γ, where Γ is the hybridization strength. Initial and final state spectral functions are recovered in the limits t → −∞ and t → +∞, respectively. Our formulation of two-time nonequilibrium Green functions within TDNRG provides a first step towards using this method as an impurity solver within nonequilibrium dynamical mean field theory.Introduction.-The nonequilibrium properties of strongly correlated quantum impurity models continue to pose a major theoretical challenge. This contrasts with their equilibrium properties, which are largely well understood [1], or can be investigated within a number of highly accurate methods, such as the numerical renormalization group method (NRG) [2][3][4][5], the continuous time quantum Monte Carlo (CTQMC) approach [6], the density matrix renormalization group [7], or the Bethe ansatz method [8,9]. Quantum impurity models far from equilibrium are of direct relevance to several fields of research, including charge transfer effects in lowenergy ion-surface scattering [10][11][12][13][14][15][16][17], transient and steady state effects in molecular and semiconductor quantum dots [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], and also in the context of dynamical mean field theory (DMFT) of strongly correlated lattice models [37][38][39], as generalized to nonequilibrium [40][41][42]. In the latter, further progress hinges on an accurate non-perturbative solution for the nonequilibrium Green functions of an effective quantum impurity model. Such a solution, beyond allowing timeresolved spectroscopies of correlated lattice systems within DMFT to be addressed [43][44][45][46][47], would also be useful in understanding time-resolved scanning tunnelling microscopy of nanoscale systems [48] and proposed cold atom realizations of Kondo correlated states [49][50][51][52], which could be probed with real-time radio-frequency spectroscopy [53][54][55].In this Letter, we use the time-dependent numerical renormalization group (TDNRG) approach [56][57][58][59][60][61][62] to calculate the retarded two-time ...

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“…II E. The main developments required for such finite bias calculations are accurate and computationally efficient solvers for the outof-equilibrium AIM in the steady-state. Such developments are still an open research direction, and important progresses have been recently made 129,[189][190][191][192] .…”

Section: E Transport Properties From Dft+negf+ctqmcmentioning

confidence: 99%

Quantum transport simulation scheme including strong correlations and its application to organic radicals adsorbed on gold

Droghetti

Rungger

2017

Phys. Rev. B

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We present a computational method to quantitatively describe the linear-response conductance of nanoscale devices in the Kondo regime. This method relies on a projection scheme to extract an Anderson impurity model from the results of density functional theory and non-equilibrium Green's functions calculations. The Anderson impurity model is then solved by continuous time quantum Monte Carlo. The developed formalism allows us to separate the different contributions to the transport, including coherent or non-coherent transport channels, and also the quantum interference between impurity and background transmission. We apply the method to a scanning tunneling microscope setup for the 1,3,5-triphenyl-6-oxoverdazyl (TOV) stable radical molecule adsorbed on gold. The TOV molecule has one unpaired electron, which when brought in contact with metal electrodes behaves like a prototypical single Anderson impurity. We evaluate the Kondo temperature, the finite temperature spectral function and transport properties, finding good agreement with published experimental results. • Define the Anderson impurity (AI) within the extended molecule by a set of interacting orbitals: ψ (ψ , , ) • Construct the projection matrix to decouple AI from bath (B): = † = AI AI,B B,AI B Solve AI model Σ AI MB ( ) Δ AI ( ), AI MB ( ) = − − Σ L − Σ R − Σ MB ( ) −1 = Tr Γ L MB † Γ R MB = B + AI + I DFT+NEGF: Extended molecule Green's function ( ) = − − Σ L − Σ R −1 DFT: Relaxed atomic structure = −1 −1 † = AI AI,B B,AI B AI ( ) = − AI − Δ AI ( ) −1 CTQMC + analytic continuation • Evaluate AI hybridization function, Δ AI , so that FIG. 2. Schematic representation of the method for the calculation of the transport properties in presence of interacting Anderson impurities.

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Extracting spectral properties from Keldysh Green functions

Cited by 13 publications

References 29 publications

Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy

Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy

Time Evolution of the Kondo Resonance in Response to a Quench

Quantum transport simulation scheme including strong correlations and its application to organic radicals adsorbed on gold

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