Correction: Eur. Phys. J. B (2022) 95:202 https://doi.org/10.1140/epjb/s10051-022-00438-2

In the original article, three equations were erroneous: Eqs. (6), (13a) and (16). We give the corrected versions of these three equations below:

$$\begin{aligned} {\mathcal {I}}_{U_{\textrm{irr}}}(k_1,k_2,k_3)&={\mathcal {I}}(k_1,k_2,k_3) - U + M^{\textrm{M}}_{k_1 k_3}(k_2-k_3)\nonumber \\&\quad +\frac{1}{2}\left[ M^{\textrm{M}}_{k_1 k_4} (k_3-k_1)+M^{\textrm{D}}_{k_1 k_4}(k_3-k_1)\right] \nonumber \\&\quad + M^{\textrm{SC}}_{k_1 k_3}(k_1+k_2), \end{aligned}$$
(6)
$$\begin{aligned} I^{\textrm{M}}_{kk'}(Q) = V(k',k,k+Q), \end{aligned}$$
(13a)
$$\begin{aligned} w^{\textrm{X}}(Q)=U + \mathrm{\mathcal {K}}^{(1)\textrm{X}}(Q). \end{aligned}$$
(16)

Since \(\textrm{sgnX}\) is no longer present in Eq. (16), the comment “with the same convention of \(\textrm{sgnX}\) as in Eq. (5).” right below it was removed as well.

Footnote 5 of the original article was pointing out an error in Ref. [35] (“We note that in Eq. (15) of Ref. [35], the term \(-U\) is erroneously missing on the right-hand side.”), which has been eventually indicated with an erratum for the article in question. This footnote has thus been removed from the original article.

For more details, we refer to Sarah Heinzelmann’s PhD thesis [1].