CM
In the literature: open
Origin of slow relaxation in the intermediate-disorder regime
In plain words
Between the clearly thermal and the apparently localized regimes, disordered chains relax extremely slowly, as power laws in time. What causes this slowness, and whether it ends at a finite time, is unclear.
Precise statement
In the random-field Heisenberg chain for disorder between about $2J$ and $W_c$, imbalance and spin autocorrelations decay as power laws or subdiffusively over many decades of time. Identify the mechanism (rare Griffiths regions, many-body resonances, or both) and predict the relaxation time $\tau(W, L)$. Answer: a theory predicting $\tau(W)$ and its $L$ dependence, verified by numerics.
What would settle it
Agreement between predicted resonance statistics and relaxation times and large-scale time evolution and eigenstate data.