  Continuous phase transitions can be classified into ones characterized by
local-order parameters and others that need additional topological constraints.
The critical dynamics near the former transitions have been extensively
studied, but the latter is less understood. We fill this gap in knowledge by
studying the transition dynamics to a parity-breaking topological ground state
called the chiral soliton lattice in quantum chromodynamics at finite
temperature, baryon chemical potential, and external magnetic field. We find a
slowing down of the soliton's translational motion as the critical magnetic
field approaches while the local dissipation rate remains finite. Therefore,
the characteristic time it takes to converge to the stationary state associated
with a finite topological number strongly depends on the initial configuration:
whether it forms a solitonic structure or not.
