报告题目：Large-Scale Modeling of Complex Quantum Systems（复杂量子系统的大尺度模拟）
A common approach to solve a problem in quantum mechanics usually starts by looking for solutions to the time-independent Schrödinger equation. Observable quantities or physical properties can be derived directly using eigenfunctions obtained from the diagonalization of the Hamiltonian matrix. However, as the costs of memory and CPU time in diagonalization processes are not linearly dependent on the dimension of the Hamiltonian matrix, this approach is unfavorable or even inapplicable for complex quantum systems. In this talk, I will show a new approach for modeling of complex quantum systems without any diagonalization. As an example, I will focus on problems in condensed matter physics and introduce the so-called tight-binding propagation method (TBPM). TBPM is based on the numerical solution of the time-dependent Schrödinger equation, with linearly scaling of the computational cost on system size. It has significant advantages in the modeling of large and complex quantum structures, ranging from mesoscopic to macroscopic level, without the requirement of any symmetry. I will give a general introduction of the method and show its applications in studying of two-dimensional materials, heterostructures, fractals, quasicrystals, and superstructures. I will also show how to combine TBPM with other well-known numerical methods such as density functional theory and molecular dynamics. At last, I will give a brief introduction of our large-scale simulation package, which will be launched soon by mid-2021.