Hey there 
Please have look at
And enclose the code you posted in triple backticks ```
Also your Julia version is rather old. I’d recommend updating to the current version 1.10.5 (I don’t think this causes your problems but it’s better to use a supported version anyways).
Can you please also provide some sample output where the vector breaks down? Is it just the vector that (over time) gets NaNs or do the Hamiltonians contains NaNs from the beginning?
Try updating your KrylovKit.jl since your are 2 versions behind. Perhaps that helps already. Otherwise try increasing the Krylov dimension.
The renormalization step in your loop should in principle be uncessary. If the norm changes (more than a couple eps) during the Krylov propagation then went wrong already because it was not unitary.