A Further Comparison of TD-DMRG and ML-MCTDH for Nonadiabatic Dynamics of Exciton Dissociation

Abstract: Tensor network methods, such as time-dependent density matrix renormalization group (TD-DMRG) and multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH), are powerful tools for simulating quantum dynamics. While both methods are theoretically exact in the limit of large bond dimensions, a recent study reported up to 60% discrepancy in their calculations for exciton dissociation. To resolve this inconsistency, we conduct a systematic comparison using Renormalizer, a unified software framework for matrix product states (MPS) and tree tensor network states (TTNS). By revisiting the benchmark P3HT:PCBM heterojunction model, we show that the observed discrepancies arise primarily from insufficient bond dimensions. By increasing bond dimensions, we first reduce the difference to less than 10%. Further refinement using an extrapolation scheme and an optimized tensor network structure lowers the difference to approximately 2%. Our results confirm both methods converge to numerically exact solutions when bond dimensions are adequately scaled. This work not only validates the reliability of both methods but also provides high-accuracy benchmark data for future developments in quantum dynamics simulations.