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

We establish a universal theory to understand quasiparticle Hall effects and transverse charge-carrier transport in organic semiconductors. The simulations are applied to organic crystals inspired by rubrene and cover multiple transport regimes. This includes calculations of the intrinsic Hall conductivity in pristine crystals, which are connected with a simple description of semiclassical electron transport that involves the concept of closed electronic orbits in the band structure, which can be easily calculated in density functional theory. Furthermore, this framework is employed to simulate temperature-dependent longitudinal and transverse mobilities in rubrene. These simulations are compared to experimental findings, providing insights into these results by characterizing the nonideality of the Hall effect due to the influence of vibrational disorder. We finally investigate the conditions for the observation of Shubnikov-de Haas oscillations in the longitudinal resistivity and quantized Hall plateaus in the transverse resistivity. A clear picture why this is not observed in rubrene is developed. These insights into classical and quantum Hall effects and their intermediates in organic semiconductors establish a blueprint for future explorations in similar systems.