CM
In the literature: open
Critical disorder and universality class of the MBL transition
In plain words
If localization does occur above some disorder strength, the transition point and how quantities behave near it are unknown. Small-computer studies disagree with theories built on rare thermal patches.
Precise statement
Assuming $W_{c}$ exists for the random-field Heisenberg chain, determine $W_{c}/J$ and the scaling near the transition (Kosterlitz-Thouless-like versus a finite correlation-length exponent $\nu$, subject to the Harris-Chayes bound $\nu \ge 2$ in $d = 1$). Answer: $W_{c}$ with uncertainty and the scaling form of the characteristic length near $W_{c}$.
What would settle it
Avalanche-stability numerics (chain coupled to an ideal bath at one end) extrapolated with a controlled scaling theory and consistent with renormalization-group predictions.