Abstract
In condensed matter physics, first-principles calculations of many-electron systems typically rely on the stationary Schrödinger equation, which uses matrix diagonalization to obtain energy eigenvalues and eigenstates. However, the computational complexity of such methods scales cubically with system size, posing challenges for studying complex systems—such as those involving defects, interfaces, superlattices, or amorphous structures with broken or extended periodicity. This talk focuses on transforming computational problems from the stationary to the time-dependent Schrödinger equation framework, thereby avoiding diagonalization and enabling large-scale simulations. The proposed method scales linearly with system size, increasing the number of simulatable atoms by several orders of magnitude. It is applicable not only to tight-binding models but also to density functional theory. Finally, recent advances in quantum spin systems, quantum computer simulations, Hubbard models, and phonon calculations are briefly discussed.