Breakdown of the orbit-like differential entanglement structure vs local potential

Determine when and how the orbit-like structure observed in the dependence of the differential entanglement entropy ΔS(l) on the local on-site potential—obtained by varying the initial phase in the slowly varying potential model—breaks down, and identify the theoretical mechanism governing this breakdown (e.g., its relation to adiabaticity).

Background

In the localized regime, the authors observe orbit-like structures when plotting ΔS(l) versus the local potential while varying the initial phase. These structures smear out and eventually disappear as the system approaches delocalization.

They explicitly state theoretical uncertainty about the conditions and mechanism for the breakdown of this structure, linking it to unclear notions of adiabaticity in such systems. Clarifying this could illuminate microscopic aspects of the MBL-to-thermal crossover.