The renormalized superperturbation theory (rSPT) approach to the Anderson model in and out of equilibrium

Abstract

The properties of current-carrying steady states of strongly correlated systems away from the linear-response regime are of topical interest. In this article, we review the renormalized perturbation theory, or renormalized SPT of reference 1 for the Anderson model. We present an extension to higher orders and compare the higher-order results with NRG calculations. Finally, we elucidate the role of Ward identities in calculating out-of-equilibrium properties and address claims made in the literature. arXiv:1610.06824v1 [cond-mat.str-el]

Leading temperature dependence of the conductance in Kondo-correlated quantum dots

“…1 of Ref. [29], it is clear that the deviation of both results is already larger than 0.8 for U = 3∆ and E d = −0.3∆. This indicates that our RPT results for U = 3∆ are nearly an order of magnitude more precise near E d = 0.…”

“…The comparison between RPT and NRG for U = 8∆ shows that the agreement does not deteriorate with increasing U in contrast to the case of IPA [27] or rSPT [24,29,30]. For example, the underestimation of the magnetic susceptibility at the symmetric point by the IPA increases to 15 % for U = 4∆, while it is only 1.4 % for U = 2∆.…”

“…In Ref. [29], a comparison between result of c ′ T calculated with NRG and rSPT including ladder diagrams was presented for U ≤ 3∆. From Fig.…”

Comment on "The renormalized superperturbation theory (rSPT) approach to the Anderson model in and out of equilibrium"

“…This is the case of some molecular system in which U is very large [13]. Moreover, since χ decreases (T 0 increases) fast when moving to the intermediate valence region ε d ∼ 0, the c ′ are considerably smaller (by a factor (T s 0 /T 0 ) 2 ) than the c. As a consequence, while the c have an increasing downward curvature as ε d increases from −U/2 to 0 [7], the c ′ have an inflexion point [1] and become in general much smaller for ε d ∼ 0. Since at the other end of the plotted values, ε d = −U/2 the coefficients are fixed by Fermi liquid properties, the end points of c ′ are rather fixed and it is hard to see deviations from any two curves of c ′ , while they are more evident if c is represented.…”

“…This difference is reduced to 2.6% when c ′ B is plotted. While the IPA might be considered acceptable for U = 3∆ and improves considerably as U is lowered [7], the main problem is that the IPA [7] (and it seems to be also the case rSPT [1]) rapidly deteriorates as U increases. In the Kondo limit −ε d , ε d + U ≫ ∆, one knows that the spectral density displays two charge-transfer peaks for ω ∼ ε d and ω ∼ ε d + U of total width 4∆ and a Kondo peak at the Fermi level of width of the order of 2 ∆ [14].…”