Kondo breakdown in multi-orbital Anderson lattices induced by destructive hybridization interference

- Novel idea of tuneability from interference between multiple non-interacting itinerant bands in the periodic Anderson model.

- The numerical results are available from a separate Zenodo repository.

- As I and one other referee pointed out in our first reports the manuscript does not adhere to the SciPost Physics author guidelines on the point

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In the resubmission the authors have supplied the numerical results producing the figures in the manuscript. However, the means of reproducing the results have not been made available, even though the calculations have been performed using publicly available open source software.

In the revised manuscript the authors have made a serious effort to address the issues raised by the referees. Unfortunately, I think the readability of the manuscript has suffered in this effort since my main point of critique was based on a misunderstanding from my side, see details below.

The current manuscript contains several sections that I think could be delegated to appendices, in favor of a more concise story in the main text. I recommend the authors to consider making appendices of the sections, "2.2.1 Multi-band SIAM vs. Multi-band PAM", "3 Theoretical motivation", and "4.2 Generality of destructive hybridization interference".

All in all, I think that the results and manuscript text now meet the criteria for publication in SciPost Physics. However, I do not think the manuscript meets the SciPost Physics criteria of reproducibility, since the NRG simulation scripts are not part of the supplemental materials distributed on Zenodo.

If the authors make the results reproducible by extending the supplemental Zenodo material and considers the comments in my report I am willing to support the manuscript for publication in SciPost Physics.

## Two-band PAM and interference effects

In my first report I raised the question how the two-band PAM differs from the single band PAM and asked the authors to clarify. The authors reply and the ensuing discussion with another referee was enlightening on this point and I now think I understand the fundamental difference between the two models. However, in my opinion, the revised manuscript remains obscure on this point.

I think the introductory sections on the two-band PAM could benefit from being more concrete and explicit. In particular I recommend the authors to explicitly include the first row of Eq. (A.1) in the method section, since this is explicitly how the authors perform the integration over lattice momenta. With this equation it is possible to realize that there are no functions $\rho_1(\epsilon)$ and $\rho_2(\epsilon)$ that can satisfy the relation
$$
G^f(z) = \int_{-\infty}^\infty d\epsilon \,
\rho^c(\epsilon)
\frac{1}{ z - \epsilon^f - \Sigma(z)
- \frac{V_1^2}{z - (\epsilon + \epsilon^c)}
- \frac{V_2^2}{z - (\epsilon + \epsilon^c)}
}
\\
\ne
\int_{-\infty}^\infty d\epsilon \,
\rho_1(\epsilon)
\frac{1}{ z - \epsilon^f - \Sigma(z)
- \frac{V_1^2}{z - (\epsilon + \epsilon^c)}
}
\\
+
\int_{-\infty}^\infty d\epsilon \,
\rho_2(\epsilon)
\frac{1}{ z - \epsilon^f - \Sigma(z)
- \frac{V_2^2}{z - (\epsilon + \epsilon^c)}
}
$$
which was the cause of confusion in my first report.

Further I think that the discussion on the small energy scale produced by the interference between the two bands could be made more informative by explicitly showing the non-interacting f-electron density of states $\rho^f(\omega)$ and how a low energy scale appears as $\alpha \rightarrow 1$ already in the non-interacting limit.

It would also be instructive to compare $\alpha=1$ and $U=0$ case for $\rho^f(\omega)$ with the single band PAM density of states from
$$
G^{f}_{SB-PAM}(z) =
\int_{-\infty}^\infty d\epsilon \,
\rho^c(\epsilon)
\frac{1}{ z - \epsilon^f - \Sigma(z) - \frac{V^2}{z - \epsilon} }
$$
and seeing that, while both are gapped, the two-band PAM has an additional sharp delta-peak resonance at $\alpha = 1$ located at $\omega = 0$.

## Claim: Scaling of low energy scale $T_0$.

With regards to the data shown in Fig. 1 the authors state

"""For small values of γ − 1, we observe an excellent agreement between the ratio determined numerically with the DMFT(NRG) and analytic expression stated in Eq. (21).""

In this regime the value of the ratio is of order unity (1) while the deviations of the numerical data from Eq. (21) is of the order 1/10. The log-scale on the y-axis obfuscates this somewhat.

I recommend the authors to weaken their claim that a 10% absolute error is an excellent agreement.

## Claim: Quantum phase transition at $\alpha = 1$

Regarding the quantum phase transition and disappearance of the low energy temperature scale $T_0$ as $\alpha \rightarrow 1$, the current presentation in the manuscript connects this to an effective Kondo lattice scale.

However, as far as I can tell, the two-band PAM undergoes a quantum phase transition as $\alpha \rightarrow 1$ already in the non-interacting ($U=0$) limit. As $\alpha \rightarrow 1$ (when $U=0$) the gap in the f-electron spectral density goes to zero, and at $\alpha = 1$ the gap closes and the system becomes metallic with a sharp resonance at $\omega = 0$.

I recommend the authors to clarify the origin of the quantum phase transition in the two-band PAM and how the phase transition at finite $U$ is connected to the "trivial" phase transition on the non-interacting limit.

- Delegate some of the discussions in the introduction to appendices.

- Explicitly state used lattice self consistency relation in the introduction, see 1st line in Eq. (A.1)

- Fig. 1: Weaken statement on "excellent agreement" given 10% absolute errors at small $\gamma - 1$.

- Plot $\rho^f(\omega)$ for $U = 0$, $|\epsilon^{c}|\ne 0$ and $\alpha = 0, 1/2, 3/4, 1, 4/3, 2, \infty$ showing how the band interference effects change with $\alpha$ and induce a low energy scale that goes to zero as $\alpha = 1$.

- Make numerical simulations reproducible by distributing the python scripts operating Ljubjana NRG on Zenodo.

- Clarify quantum phase transition claim

- Fig. 2: The color descriptions in the figure caption does not agree with the figure legend.

Ask for minor revision