Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

Please see the earlier report.

Please see the earlier report.

I thank the Authors for their detailed reply to my earlier report. I believe, there have been a few misunderstandings that may arise from my inadequate choice of wordings. Below, I reply to the Authors’ comments in details.

1. I agree that the results presented in Sec. 4 and 5, can only be guessed beforehand once the effective Hamiltonian is known, and not from the initial interacting Hamiltonian. In my earlier report, I stressed this point couple of times that the derivation of the simple effective Hamiltonian from the initial complicated Hamiltonian is the main result of the Manuscript, which I find very elegant and interesting, and therefore must deserve a publication in some form on its own. However, as a reader, after going through the derivation of Sec. 3 and the form of the effective Hamiltonian, the results of Sec. 4 and 5 do not stand-out on their own, as they are derived from the effective Hamiltonian itself, and not from the full Hamiltonian (specifically, the inhibition dynamics of Sec. 4). Moreover, there is no comparison presented between the dynamics of the full Hamiltonian and that of the effective one, especially for $\kappa/\omega = 0.5$ (Fig. 3 bottom panel), as this choice of $\kappa/\omega$ is close to the borderline of the validity of the perturbative calculation.


2. I am still unconvinced about the generality in the choice of system parameters, as they must follow stringent conditions for the perturbative treatment to be valid.


3. I understand, my choice of the word ‘thermodynamic limit’ have caused some confusions. My concern about the ‘thermodynamic limit’ was not about the Hamiltonians (effective or the original one). I was concerned, as the number of excitations (or energy) in the initial cluster-1 (single cluster of size 1) state does not grow linearly with system-size. But, now I understand that this is not an issue, as the extensivity of the initial state is not required for the ballistic growth of the cluster-size, but only required for a thermalizing dynamics (which is beyond the scope of the present manuscript, of course). However, as I said in the earlier report, the initial states having cluster of size 1 are very special. The number of such states only grows linearly with the system-size, while the atom-only Hilbert space dimension grows as $\sim N^2$ without considering the local phonon degrees of freedom. Rest of the states follow ballistic dynamics as seen in the manuscript. Therefore even a small perturbation in the initial state, and/or small couplings to other states (that are ignored in the perturbative expansion) may hinder the inhibition to the ballistic growth, resulting in ballistic (or may be even thermalizing) dynamics. In experiments, getting rid of such small perturbations from the pure cluster-1 state can indeed be very difficult.


3. In the minor points, the comment about the thermodynamic limit of the band structure was not about that of the effective Hamiltonian, but about the full Hamiltonian of Eq. 7. I should have been more clear. I apologize to the Authors for that. Specifically, I was curious whether the appearance of the bound state in the band structure (of Hamiltonian Eq. 7), as seen in the bottom panels of Fig. 2, survives large size limit or not.

To summarize, I stand by my earlier assessment, as the manuscript, in its present form, in my opinion, does not meet the acceptance criteria of SciPost Physics.