  Quantum speed limit (QSL) is the lower bound on the time required for a state
to evolve to a desired final state under a given Hamiltonian evolution. Three
well-known QSLs exist Mandelstam-Tamm (MT), Margolus-Levitin (ML), and dual ML
(ML$^*$) bounds. We consider one-dimensional systems that undergoes
delocalization-localization transition in the presence of quasiperiodic and
linear potential. By performing sudden quenches across the phase boundary, we
find that the exact dynamics get captured very well by QSLs. We show that the
MT bound is always tighter in the short time limit for any arbitrary state,
while the optimal bound for the time of orthogonalization (time required to
reach the orthogonal state) depends on the choice of the initial state.
Further, for extreme quenches, we prove that the MT bound remains tighter for
the time of orthogonalization, and it can qualitatively describe the
non-analyticity in free energy for dynamical quantum phase transition (DQPT).
Finally, we also demonstrate that the localization-delocalization transition
point can be exactly identified from QSLs, whose computation cost is much less
compared to many other diagnostic tools.
