  The accurate description and robust computational modeling of the
nonequilibrium properties of quantum systems remain a challenge in condensed
matter physics. In this work, we develop a linear-scale computational
simulation technique for the non-equilibrium dynamics of quantum quench
systems. In particular, we report a polynomial-expansion of the Loschmidt echo
to describe the dynamical quantum phase transitions of noninteracting quantum
quench systems. An expansion-based method allows us to efficiently compute the
Loschmidt echo for infinitely large systems without diagonalizing the system
Hamiltonian. To demonstrate its utility, we highlight quantum quenching
dynamics under tight-binding quasicrystals and disordered lattices in one
spatial dimension. In addition, the role of the wave vector on the quench
dynamics under lattice models is addressed. We observe wave vector-independent
dynamical phase transitions in self-dual localization models.
