Renormalized parameters and perturbation theory for ann-channel Anderson model with Hund’s rule coupling: Asymmetric case

Abstract

We explore the predictions of the renormalized perturbation theory for the n-channel Anderson model, both with and without Hund's rule coupling, in the regime away from particle-hole symmetry. For the model with n = 2 we deduce the renormalized parameters from numerical renormalization group calculations, and plot them as a function of the local occupation of the impurity site n d . From these we deduce the orbital, spin and charge susceptibilities, Wilson ratios and quasiparticle density of states at T = 0 in the different parameter regimes, which gives a comprehensive overview of the low energy behavior of the model. We compare the difference in Kondo behaviors at the points where n d = 1 and n d = 2. One unexpected feature of the results is the suppression of the charge susceptibility in strong correlation regime over the occupation number range 1 ≤ n d ≤ 3.

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

“…The Anderson model with U 12 = U can be mapped into a SU(4) Kondo model also in the case with particle-hole symmetry with n d,1 = n d,2 = 1. 31 In this case the operators in the model correspond to a 6-dimensional representation of SU(4) in contrast to the mapping for the spin/pseudospin degenerate model with n d,1 = n d,2 = 0.5 where the operators correspond to the fundamental (4-dimensional) representation of SU (4).…”

“…For U ≫ D, there is a regime where we do find SU(4) symmetry with U 12 < U provided U 12 is also greater than, or comparable with, the half bandwidth D. This is consistent with the derivation of an SU(4) Coqblin-Schrieffer model based on a Schrieffer-Wolff transformation. 5,31,32 We note that there is not a unique SU(4) Kondo model for the double quantum dot. The Anderson model with U 12 = U can be mapped into a SU(4) Kondo model also in the case with particle-hole symmetry with n d,1 = n d,2 = 1.…”

“…The question arises as to whether the ratioŨ 12 /Ũ would approach the value 1 in this range if we increase the value of U still further. As U/πΓ > 20 = 0.2/D (D = 31,32 The question arises as to whether this mapping still holds if U 12 < U , and if it also applies to a parameters with U < D. In Fig. 7 we give the results forŨ 12 /Ũ as a function of U 12 /U for ε d = −3πΓ and U/D = 0.12, 0.2, 0.5, 1, 10, 100.…”

“…With the choice ε d = −U 12 /2 for U 12 /πΓ ≫ 1 we have n tot ∼ 1 but not precisely equal to 1. In an earlier study of the SU(4) version of this model 31 we calculated the renormalized parameters keeping n d,tot strictly equal to 1. In that case we obtained the resultŨ /πΓ = 0.66665 asymptotically for large U in very accurate agreement with the prediction from Eq.…”

“…33 There are two such SU(4) Kondo models corresponding to the total occupation numbers, n d,tot = 1 and n d,tot = 2. For the SU(4) model with n d,tot = 1 we find T * /πΓ = T K /πΓ = 0.096, which is greater than but of the same order of magnitude as the value T * /πΓ ∼ 0.055 deduced from the results in Fig.…”