论文标题
评论“共鸣引起的熵在牢固无序系统中的数量熵的增长”
Comment on "Resonance-induced growth of number entropy in strongly disordered systems"
论文作者
论文摘要
我们对Ghosh和Žnidarič最近的论文发表评论（Phys。B105，144203（2022）），研究了Heisenberg模型中数字熵的增长$ s_n $，并在量子淬火后随机磁场。作者提出了有关时间$ t $和亚凝技术饱和值的中间力量增长的论点，并声称其结果与多体定位（MBL）有关强障碍的结果一致。我们表明，这些解释与其他最近的研究不一致，并通过对数值数据的分析进行了讨论的特定问题。我们特别指出的是，（i）饱和值$ \ widetilde {s} _n（l，w）$固定长度$ l $仅在上面的“ ergodic value”界限，并且已经远低于$ w \ ll 1 $的该值。此外，饱和值可以用$ L $显示非单调缩放。 (ii) Power-law fits $S_N(t)\sim 1/t^α$ -- with $α=1$ expected based on the resonance model described in the paper -- yield a system-size dependent exponent $α$ while fits $S_N\sim \frac{1}{W^3}\ln\ln t$ do hold independent of system size and over several orders of magnitude in time. （iii）我们还认为，对于有效共振模型效果最佳并预测数字熵的饱和的情况，同样的是von-neumann熵，即〜在考虑的尺度上的动力学是单个粒子类型的，并且与MBL无关。
We comment on the recent paper by Ghosh and Žnidarič (Phys. Rev. B 105, 144203 (2022)) which studies the growth of the number entropy $S_N$ in the Heisenberg model with random magnetic fields after a quantum quench. The authors present arguments for an intermediate power-law growth in time $t$ and a sub-ergodic saturation value, claiming consistency of their results with many-body localization (MBL) for strong disorder. We show that these interpretations are inconsistent with other recent studies and discuss specific issues with the analysis of the numerical data. We point out, in particular, that (i) the saturation values $\widetilde{S}_N(L,W)$ for fixed length $L$ are only bounded from above by 'the ergodic value' and are already far below this value for $W\ll 1$. Furthermore, the saturation values can show non-monotonic scaling with $L$. (ii) Power-law fits $S_N(t)\sim 1/t^α$ -- with $α=1$ expected based on the resonance model described in the paper -- yield a system-size dependent exponent $α$ while fits $S_N\sim \frac{1}{W^3}\ln\ln t$ do hold independent of system size and over several orders of magnitude in time. (iii) We also argue that for the cases where the effective resonance model works best and predicts a saturation of the number entropy, the same applies to the von-Neumann entropy, i.e.~the dynamics at the considered scales is of single particle type and unrelated to MBL.
