  The dynamic critical exponent $z$ characterizes the finite-size gap in
gapless quantum many-body systems. We establish a rigorous lower bound $z \geq
2$ for frustration-free Hamiltonians on any lattice in any spatial dimension,
given that their ground state exhibits a power-law decaying correlation
function. This bound applies to representative classes of frustration-free
Hamiltonians, including Rokhsar-Kivelson Hamiltonians, which are in one-to-one
correspondence to Markov chains with locality, as well as parent Hamiltonians
of critical projected entangled pair states with either a unique ground state
or topologically degenerate ground states, and Hamiltonians with a plane-wave
ground state.
