Buildup of the Kondo effect from real-time effective action for the Anderson impurity model

Bock, Sebastian; Liluashvili, Alexander; Gasenzer, Thomas

doi:10.1103/physrevb.94.045108

Cited by 15 publications

(18 citation statements)

References 130 publications

(166 reference statements)

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“…This topic has been addressed before within several approaches, including the non-crossing approximation [26,63], conserving approximations [64] and within CTQMC for quantum dots out of equilibrium [32]. Related work on the temporal evolution of the spin-spin correlation function in the Kondo model and thermalization in the Anderson impurity model following initial state preparations has also been carried out [65,66].…”

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confidence: 99%

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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confidence: 99%

Time Evolution of the Kondo Resonance in Response to a Quench

Nghiem

Costi

2017

Phys. Rev. Lett.

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“…How this can happen can be understood specifically from Eq. (41), which shows that initially the occupations grow towards half filling -away from the stationary value -as dictated by Π ∞ . Indeed, in Fig.…”

Section: Transient Effectsmentioning

confidence: 89%

“…4(b) we compare the transient currents obtained by the T -flow with those obtained in Ref. [41] using a two-particle-irreducible effective action (2PI) approach at low temperature T = 0.1Γ and intermediate interaction U = 4Γ . We find overall good agreement.…”

Section: Transient Effectsmentioning

confidence: 90%

Renormalization group for open quantum systems using environment temperature as flow parameter

Nestmann,

Wegewijs

2021

Preprint

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We present the T -flow renormalization group method, which computes the memory kernel for the density-operator evolution of an open quantum system by lowering the physical temperature T of its environment. This has the key advantage that it can be formulated directly in real time, making it particularly suitable for transient dynamics, while automatically accumulating the full temperature dependence of transport quantities. We solve the T -flow equations numerically for the example of the single impurity Anderson model. In the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger, we benchmark using results obtained by the functional renormalization group, density-matrix renormalization group and the quantum Monte Carlo method. Here we find quantitative agreement even in the worst case of strong interactions and low temperatures, indicating the reliability of the method. For transient charge currents we find good agreement with results obtained by the 2PI Green's function approach. Furthermore, we analytically show that the short-time dynamics of both local and non-local observables follow a "universal" temperature-independent behavior when the metallic reservoirs have a flat wide band.

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“…We expect higherorder predictor-corrector methods as used in Ref. [66] to lead to better convergence properties, which may improve the area of application of the present method.…”

Section: Resource Consumption and Possible Improvementsmentioning

confidence: 89%

“…A powerful non-perturbative method for N -component field theories consists in expanding Γ 2 in powers of 1/N 11,31 . When taking into account diagrams up to next-to-leading (NLO) order, this approximation has been shown to outperform other beyond-mean-field approximation schemes in ultracold Fermi 58 and Bose gases 53,59,60 , including optical lattices 61,62 , and it has been successfully applied to a myriad of problems such as thermalization of bosonic 12 and fermionic quantum fields 14 , time evolution of quasiparticle spectral functions 63 , critical exponents in the O(N ) model 64 , prethermalization and heating in Floquet systems 65 , and the Kondo effect in the Anderson impurity model 66 . Remarkably, it has even been able to capture regimes of very large infrared fluctuations close to nonthermal fixed points [67][68][69][70] , as well as regimes of strong couplings even for rather small values of N 70 .…”

Section: Non-perturbative Expansionmentioning

confidence: 99%

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

Schuckert¹,

Orioli²,

Berges³

2018

Phys. Rev. B

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We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D longrange interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased. arXiv:1806.02347v2 [cond-mat.quant-gas]

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Buildup of the Kondo effect from real-time effective action for the Anderson impurity model

Cited by 15 publications

References 130 publications

Time Evolution of the Kondo Resonance in Response to a Quench

Time Evolution of the Kondo Resonance in Response to a Quench

Renormalization group for open quantum systems using environment temperature as flow parameter

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

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