  In organic semiconductors working under ambient circumstance, there are
remarkable quantum effects lack of comprehensive understanding, and an exotic
composite particle named charge transfer (CT) exciton is normally regarded as
the key ingredient. Another essential substance is the phonons stemming from
intra- and inter-molecular vibrations, and the relevant diagonal
electron-phonon couplings give rise to spatial localization and the
off-diagonal couplings refer to the dispersion of electron wavefunctions. In
this work, we first propose a toy model based upon the fracton physics to
phenomenologically unveil the coherent motion of CT excitons followed by
resonant phonons in the aggregates. Based on this model, a generic scenario of
hierarchical quantum effects is described in various material systems. To
examine whether the fracton model can be applicable in practice, we calculate
the out-of-time-ordered correlator (OTOC), a quantum dynamic measurement of the
entanglement entropy, of CT excitons by the adaptive time-dependent density
matrix renormalization group algorithm. On the basis of three commonly-used
realistic models in organic materials with two competing interactions taking
into account, we investigate the irreducible roles of CT excitons and aggregate
phonons in the ultrafast charge transfer, the coherent polaron hopping, and the
dissociation of triplet pairs, respectively. Our theory unifies the charge,
exciton, spin and phonons into a single framework, which may help clarify the
complicated and diverse quantum effects in organic semiconductors.
