arXiv:1903.06173 - Githubissues

Summary

In contrast with quantum scars in PXP, which is the low entangled eigenstate of static Hamiltonian, here the author denote the low entangled eigenstate of evolution/Floquet operator as dynamical scar states, since they are just steady state with time evolution.
Fracton circuit setup: stroboscopically repeating circuit on 1D spin 1 chain with three leg gates.
The author consider PBC here and conclude that scar states is polynomial in size in contrast with 1904.04815. PBC is utilized since translation invariant can exclude the effect from random matrix and attribute the scar states to fracton dynamics. In general, one scar state in one symmetry sector (P,Q).
a randomly chosen basis of initial conditions leads to two fairly sharp entropy bands, with the lower band having a clearly subthermal entropy.
Scar states feature an agglomerated fracton peak for physical observables, $S_z$ in the paper, similar to MBL states.
The authors also tried to compute quantum fidelity between two density operators, one from pure scar state, and the other is from so called minimal product states density matrix of given symmetry sector.

I still doubt the fact that the overlap between scar states and general random product states is surprisingly large compared to the Hilbert space dimension ratio. This should be shown carefully with at least some finite size scaling. It cannot be proven by only numerical data with L=9. Since in this case, the ratio of number of scar states over normal states is not so small, and it is expected to have some states evolve to low saturating EE. This is not a decisive evidence that such thing also happen in thermodynamic limit.