Renormalized parameters for impurity models

Abstract

Abstract. We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective levelǫ d , an effective hybridizatioñ V , and a quasiparticle interactionŨ . The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a FalikovKimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a FalikovKimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.PACS. 71.10.-w Theories and models of many-electron systems -71.27.+a Strongly correlated electron systems; heavy fermions -75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions

Analysis of low-energy response and possible emergent SU(4) Kondo state in a double quantum dot

“…24,26 The temperature dependence of the parameters can be extracted from the NRG calculations for an iteration N , such that the corresponding temperature is…”

“…We can hence describe the low energy behavior in terms of well defined quasiparticles and their interactions. We have shown in earlier work 24,25 in the absence of a magnetic field that these quasiparticles can be taken to correspond to renormalized versions of the parameters that specify the bare model,ε d,i,σ ,Γ i ,Ũ i andŨ 12 . The Hamiltonian describing the low energy fixed point and the leading irrelevant correction terms then has the same form as the original model, but with the bare parameters replaced by the renormalized ones.…”

“…We have described in earlier work how these can be deduced from an analysis of the low energy fixed point in a numerical renormalization group (NRG) calculation. 24,25 We apply the method to the model being investigated here and describe the results of these calculations in detail in the next section. We use Λ = 6 (this comparatively large value gives accurate estimates for the renormalized parameters as can be checked in the case of a single impurity model) and typically retain 4000 states in our NRG calculations.…”

“…These can be determined from an analysis of the low energy fixed point in a numerical renormalization group 22,23 (NRG) calculation. 24,25 Once these have been determined several response functions, such as the spin and charge susceptibilities at zero temperature and the linear conductance through the dots, can be calculated from exact expressions for these quantities in terms of these renormalized parameters. By comparing with exact Bethe ansatz results it has been shown that very accurate numerical results can be obtained from these calculations.…”

“…By comparing with exact Bethe ansatz results it has been shown that very accurate numerical results can be obtained from these calculations. 24,26,27 Furthermore leading order corrections to some of these results can be determined exactly using these parameters within a renormalized perturbation theory (RPT). 28 We use this technique in this paper to examine the circumstances in which the low energy behavior could correspond to an SU(4) model due to degenerate spin and inter-dot (orbital) fluctuations.…”