Do PXP scar eigenstates survive as the chain becomes infinite
In plain words
The special non-thermal states have been seen only in chains of a few dozen atoms. It is unknown whether they remain special in an infinitely long chain.
Precise statement
In the PXP chain, define the fidelity density $f(t) = -\lim_{L \to \infty} (1/L) \ln \mid\langle \mathrm{Z2}\mid \exp(-i H t/\hbar) \mid\mathrm{Z2}\rangle\mid^{2}$. Is $f$ at the first revival time strictly smaller than its time-averaged plateau value as $L \to \infty$? And does a tower of about $L+1$ eigenstates with entanglement $S = O(\ln L)$ and Z2 overlap exceeding that of typical eigenstates at the same energy by a factor $\exp(+a L), a > 0$, persist? Answer yes or no for each.
What would settle it
An exact construction of the scar tower at all L, or infinite-system tensor-network computation of f(t) showing convergence of the revival dip with bond dimension.