the transition temperature towards a given ordered state. The resulting flow of the couplings in the density-wave channels as a function of $t=\log\frac{W}{E}$, where $W$ is the bandwidth and $E$ the running energy scale, takes the form

\[eq:channel-interference-couplings\] $$\begin{aligned}
  \dot{\Gamma}_\mathrm{SDW}&= (\Gamma_\mathrm{SDW})^2\pm 2u_3(u_1-u_2-u_4){~ ,}\\ 
  \dot{\Gamma}_\mathrm{CDW}&= (\Gamma_\mathrm{CDW})^2\mp 2u_3(u_1+u_2-u_4) {~ .}\end{aligned}$$

The couplings $u_i$ refer to different intraband and interband processes that are connected to the couplings in spin and charge channel according to Eq. . If the second term were zero, this would result in the usual logarithmic divergence $\Gamma=\Gamma_0/(1-\Gamma_0\log\frac{W}{E})$ of the coupling in the respective channel. Hence the presence of the second term implies corrections due to channel interference that are intrinsic to the model as long as the interband pair-hopping process which is associated with $u_3$, and involves a momentum transfer of $2{\boldsymbol{Q}}$, is effective. Motivated by the structure of Eq. , we used $u_3^{(0)}$ as a measure of channel interference in our brief analysis, where we tuned the bare couplings such that the instability in the channel under consideration is favored within the mean-field description, while the bare couplings in the competing channels were tuned to zero. We then kept the bare value of the coupling in a given 