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13 (we shall use II to indicate this reference). Other details not given in the present paper, like the analytic solution of the AAS, can be found in Ref. 10.
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85099494114
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j,k,σ.
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In that Appendix, the ν(α, k, σ, ±u) in the item 2(b) of Rule C.2 should be changed into V(α, k, σ, ±u).
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84885039058
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n appears also in the perturbation expansion contribution of any graph of order n, i.e. with n internal edges (cf. the cumulant expansion for the Ising model in Ref. 14, where this sign has been included in the interaction constant in its Eq. (2)) We have then added a factor (- 1) to every internal edge, and therefore this extra factors would only change the sign of a graph's contribution when it is of odd order. This sign appears explicitly in the expansion of the PAM in I (cf. Eqs. (3.8) and (3.11) of that reference) but it was left out from the diagrams contribution by an oversight. Note that this sign does not depend on the Fermionic character of the X operators.
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18
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84885084357
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To simplify the notation we use Δ(x) = 0 when x ≠ 0 and Δ(0) = 1.
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84885080855
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ap, and employing these approximate cumulants we calculate the lattice Green's functions. This opens the possibility of applying the method to a broad class of physical problems governed by the Kondo scale: quantum dots, Anderson impurity problems, Kondo insulators and intermediate and heavy fermion problems.
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