Time Evolution of the Kondo Resonance in Response to a Quench

Abstract

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 ...

Transient dynamics in interacting nanojunctions within self-consistent perturbation theory

“…It should be remarked that the convergence time increases with U/Γ. In this respect it is interesting to analyze the convergence in time of the Kondo resonance, an issue that has been addressed in previous works [63,92]. One would expect this convergence time to be of the order of T T ,…”

“…The most interesting and general coherentinteracting regime constitutes a great theoretical challenge. This regime has been addressed using several complementary approaches: diagrammatic techniques [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], quantum Monte-Carlo (MC) [48][49][50][51][52][53][54][55], timedependent NRG [56][57][58][59][60][61][62][63], time-dependent DFT [64][65][66][67][68][69][70] among others [71][72][73][74][75].However, all of these techniques as they are actually implemented have some limitations. For instance, numerically exact methods like quantum MC are strongly time-consuming, require finite temperature and typically do not allow to reach long time scales.…”

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

“…Below, we derive expressions for A(ω, t) for the choices t = t 1 and t = (t 1 + t 2 )/2 within TDNRG and compare these with the results for the case t = t 2 studied in Ref. 30.…”

“…V, while the choice t = t 1 is encountered, for example, in timedependent transport through quantum dots 32,37 . The choice t = t 2 has previously been considered 24,30 in the TDNRG to time-evolve spectral functions to infinite times, required, for example, in the context of applications to steady state nonequilibrium transport within the scattering states NRG approach 5 . Below, we derive expressions for A(ω, t) for the choices t = t 1 and t = (t 1 + t 2 )/2 within TDNRG and compare these with the results for the case t = t 2 studied in Ref.…”

“…4(c), 4(f) and 4(i)]. These have been described elsewhere 30 and are in part due to the use of a Wilson chain in the TDNRG calculations 25,26,54 and in part due to the broadening procedure, see Appendix C.…”