The Time-Dependent Density Matrix Renormalization Group Method for Nonadiabatic Dynamics and Electronic Dynamics

Recent advances in experimental techniques have enabled precise characterization of fundamental nonadiabatic and even electronic dynamics in molecules, on ultrafast time scales reaching femtosecond to attosecond resolution. However, accurate theoretical simulation of these ultrafast chemical dynamics processes in large systems remains challenging, largely due to the overwhelming number of degrees of freedom (DoFs) and the pronounced many-body correlations. In recent years, by leveraging efficient decomposition schemes for high-dimensional wave function and operator tensors, the time-dependent density matrix renormalization group (TD-DMRG) has emerged as a powerful and accurate quantum dynamics method for simulating nonadiabatic and electron dynamics in large chemical systems, in conjunction with realistic electron/exciton-vibration/phonon models or ab initio quantum chemistry many-electron Hamiltonians. This review outlines the fundamentals of TD-DMRG for chemical dynamics, covering matrix product state/operator (MPS/MPO) frameworks and algorithms from ground-state calculations to time evolution. We discuss thermal/environmental effects and compare TD-DMRG with other tensor network methods such as multiconfiguration time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH). Demonstrated applications include simulations of pyrazine absorption, singlet fission in rubrene crystal, and charge migration in chloroacetylene cation. These show TD-DMRG's capability for modeling complex ultrafast processes from femtoseconds to attoseconds with controlled accuracy.