Comparison of Matrix\nProduct State and Multiconfiguration\nTime-Dependent Hartree Methods for Nonadiabatic Dynamics of Exciton\nDissociation

The excited-state dynamics of organic molecules, molecular\naggregates,\nand donor–acceptor clusters is typically governed by the interplay\nof electronic excitations and, due to their flexibility and soft bonding,\nby the interaction with their vibrations. This interaction in these\nsystems can be characterized by a few relevant electronic states that\nare coupled to numerous vibrational normal modes, encompassing a vast\nconfigurational space of the molecules. The full quantum simulation\nof these type of systems has been long dominated by the multiconfiguration\ntime-dependent Hartree (MCTDH) approach and its multilayer variants,\nwhich are considered the gold standard in the presence of electron-vibration\ncoupling with a large number of modes. Recently, also the matrix product\nstate ansatz (MPS) with appropriate time-evolution schemes has been\napplied to these types of Hamiltonians. In this article, we provide\na numerical comparison of excited-state dynamics between the MCTDH\nand MPS approaches for two electron-vibration coupled systems. Notably,\nwe consider two models for exciton dissociation at a P3HT:PCBM heterojunction,\ncomprising two electronic states and 100 vibrational modes, and 26\nelectronic states and 113 vibrational modes, respectively. While both\nmethods agree very well for the first model, more pronounced deviations\nare found for the second model. We trace back the divergence between\nthe methods to the different way entanglement is treated.