Whether the KL-divergence crossing of minimal-deviation distributions directly probes the MBL transition

Determine whether the crossing in the Kullback–Leibler divergence between the distributions of the extreme-magnetization minimal deviation in the Heisenberg (Delta=1) and XX (Delta=0) chains directly coincides with and probes the many-body localization transition in the random-field XXZ chain.

Background

The authors discuss various diagnostics for the ergodic–MBL transition. Prior work reported that the Kullback–Leibler divergence between the distributions of the minimal deviation of local magnetization in the Heisenberg and XX limits exhibits a crossing interpreted as an extreme-value transition.

It remains to be clarified whether this crossing is a faithful indicator of the MBL transition itself, which would establish the diagnostic as a direct probe of the transition.

References

We note also that in Ref., it was shown that the KL divergence between the minimal deviation distributions in the Heisenberg and the XX chains show a crossing that signals an extreme value transition, but it is yet to be clarified whether this is directly probing the MBL transition.

— Interaction-Driven Instabilities in the Random-Field XXZ Chain (2403.09608 - Colbois et al., 14 Mar 2024) in Supplemental Material, Section "Extreme magnetization"