Lifetime of exact scar states under generic weak perturbations
In plain words
Some models have exactly known non-thermal states, but any realistic small disturbance should eventually destroy them. The question is how long they survive as the disturbance gets weaker.
Precise statement
For a model with an exact scar tower (e.g. the spin-1 XY chain or the AKLT chain) perturbed by a generic local term $\epsilon V$, determine the decay time $\tau(\epsilon)$ of revivals or scar-state fidelity with $L\to\infty$ before $\epsilon\to 0$: Fermi golden rule $\tau\sim\epsilon^{-2}$, or parametrically longer. Answer: the exponent or functional form.
What would settle it
Matching upper and lower bounds on $\tau(\epsilon)$ in the thermodynamic limit, checked numerically.
Status in the literature
Unverified note
Rigorous slow-thermalization bounds exist (Lin, Chandran, Motrunich 2020) and were tightened in 2026 (arXiv:2602.21962); matching bounds on the actual decay are missing.