Linear-scale simulations of quench dynamics

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.