Reply to 'Comment on 'Nonequilibrium steady state phases of the interacting Aubry-Andre-Harper model''

摘要

In Ref. [1], we studied the interacting AAH model up to ～100 sites and obtained a phase diagram featuring superdif-fusive spin transport for small values of the quasiperiodic potential strength λ and weakly subdiffusive spin transport at larger values of λ. We exhibited structure in the quantum mutual information as a function of λ and showed that the butterfly speed was only weakly related to changes in spin transport. We also indicated that we "...originally expected a diffusive regime for weak potential strength but did not observe it in the system sizes studied." By going to 20× larger system sizes, Ref. [2] has improved our proposed phase diagram by exhibiting the expected diffusive behavior at very large system size. At small values of the quasiperiodic potential strength, we agree that this is likely explained by the relatively weak effects of integrability breaking. However, at λ = 1 there is no obvious small parameter and the model is still seemingly well separated from the localization transition at λ ～ 1.7. Absent any special structure, one would expect the model to be generically nonintegrable with a ther-malization length of the order of the lattice spacing. This expectation appears consistent with the order of one value of the diffusion constant at λ = 1 (～0.3 from rough visual estimate based on Fig. 1(a) of Ref. [2]). In such a situation, it would be surprising if one needed to access thousands of sites to see the asymptotic behavior unless the dynamics was substantially slowing with increasing λ. Our other observations, including the structure of the quantum mutual information as a function of λ and the butterfly speed of the system being only weakly related to spin transport, are not affected.