English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We comment on the recent paper by Ghosh and \v{Z}nidari\v{c} (Phys. Rev. B105, 144203 (2022)) which studies the growth of the number entropy $S_N$ in theHeisenberg model with random magnetic fields after a quantum quench. Theauthors present arguments for an intermediate power-law growth in time $t$ anda sub-ergodic saturation value, claiming consistency of their results withmany-body localization (MBL) for strong disorder. We show that theseinterpretations are inconsistent with other recent studies and discuss specificissues 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 $L$ areonly bounded from above by 'the ergodic value' and are already far below thisvalue for $W\ll 1$. Furthermore, the saturation values can show non-monotonicscaling with $L$. (ii) Power-law fits $S_N(t)\sim 1/t^\alpha$ -- with$\alpha=1$ expected based on the resonance model described in the paper --yield a system-size dependent exponent $\alpha$ while fits $S_N\sim\frac{1}{W^3}\ln\ln t$ do hold independent of system size and over severalorders of magnitude in time. (iii) We also argue that for the cases where theeffective resonance model works best and predicts a saturation of the numberentropy, the same applies to the von-Neumann entropy, i.e.~the dynamics at theconsidered scales is of single particle type and unrelated to MBL.

Comment on "Resonance-induced growth of number entropy in strongly disordered systems"