  In arXiv:2001.03419 we introduce a universal error bound for constrained
unitary dynamics within a well-gapped energy band of an isolated quantum
system. Here, we provide the full details on the derivation of the bound. In
addition, we generalize the result to isolated quantum many-body systems by
employing the local Schrieffer-Wolff transformation, obtaining an error bound
that grows polynomially in time. We also generalize the result to Markovian
open quantum systems and quantitatively explain the quantum Zeno effect.
