Thermodynamic extrapolation of the nonlocal-magic dome

Determine whether the height of the finite-size dome in disorder-averaged min-relative nonlocal magic continues to grow linearly or logarithmically with system size, or instead eventually saturates at larger system sizes.

Background

The disorder-averaged min-relative nonlocal magic develops a dome whose height increases and whose position shifts toward stronger disorder over the system sizes accessible to the numerical study. The authors compare linear-in-system-size and linear-in-logarithmic-size fits, but both describe the limited data comparably well.

Because the available sizes do not discriminate between these scaling forms or rule out saturation, the thermodynamic behavior of the dome height is left unresolved. This question concerns the extrapolation of the Schmidt-spectrum mismatch measured by nonlocal magic, not the location of the thermodynamic MBL transition.