The authors numerically study the dynamics in a quasiperiodic (QP) interacting spin chain, which shows a MBL like transition as a function of the strength of the QP potential.
In their introduction the authors claim:
"The aim of the present work is to investigate the differences between purely random
and quasi-periodic disorder at system sizes inaccessible to exact diagonalization, using the
newly developed numerical technique of the time-dependent variational principle as applied
to matrix product states"
This statement is however misleading, since dynamics in QP interacting systems was studied using MPS based method in both  (L=100-200) and 10.1073/pnas.1800589115, for systems of up to 800 sites (cf, to L=50 that the authors use in this work). In fact one of the accents of 10.1073/pnas.1800589115 is on finite-size effects and comparison to the disordered case.
However, my main concern is not even with the originality of the work, but with the validity of its results. The authors use a very low bond dimension (xi<64, compared to xi=1000-2000, many time used in TEBD), and their method (1-site TDVP) doesn't allow them to estimate the discarded weight. Moreover, the comparison between the two shown bond-dimensions are done on a logarithmic scale and for different "disorder" realizations, which doesn't allow to estimate the time until which the results are reliable.
From Fig 1 it is obvious that this time is not longer than t~100 (which is also probably a conservative estimate). This can also seen from the comparison to TEBD, which the authors provide in their reply. Although the graph is also on a log-log scale, for W=4, the divergence with TEBD occurs already at t<100, where TEBD results appear to converge, as far as one ca n judge from this plot. While one can see that TEBD saturates the bond dimension 256 already at times t=20, the actually meaningful information is the accumulated discarded weight, which the authors don't provide.
As on can see from Fig 3 for t<100 and W=4, the drift in the dynamical exponent, which is one of the main results of the work is not significant, and in any case probably lies within the error bars (which are not shown for some reason). For W>5 the oscillations in the exponent do not allow to extract a coherent message, though the convergence issues I raised above, are presumably better there.
Another issue, which is not discussed in the paper is the convergence with respect to the time-step. Following a request by the first referee the authors do specify the time-step dt=0.1, in their reply, but don't provide any evidence that this time-step is sufficient to go to t=300 and W=8 for example.
In view of the above I agree with the report of the first referee that the conclusions of this work are most probably based on not converged data, and are therefore doubtful. I therefore do not think that the paper stands by the standards of SciPost.