  A sudden quantum quench of a Bloch band from one topological phase toward
another has been shown to exhibit an intimate connection with the notion of a
dynamical quantum phase transition (DQPT), where the returning probability of
the quenched state to the initial state---i.e. the Loschmidt echo---vanishes at
critical times $\{t^{*}\}$. Analytical results so far are limited to two-band
models, leaving the exact relation between topology and DQPT unclear. In this
work, we show that for a general multi-band system, a robust DQPT relies on the
existence of nodes (i.e. zeros) in the wavefunction overlap between the initial
band and the post-quench energy eigenstates. These nodes are topologically
protected if the two participating wavefunctions have distinctive topological
indices. We demonstrate these ideas in detail for both one and two spatial
dimensions using a three-band generalized Hofstadter model. We also discuss
possible experimental observations.
