  The role of nonlocal electron-phonon couplings (EPC) in organic
semiconductors has the been center of interest recently. Several irreconcilable
scenarios coexist for the description of the nonlocal EPC, such as
phonon-assisted (PA) transport, transient localization (TL), and band-like (BL)
transport. In this Letter, we present a nearly exact numerical study for the
carrier mobility of the one-dimensional Holstein-Peierls model using finite
temperature time-dependent matrix product states approach. We are able to
locate the PA, TL and BL regimes as a function of the electronic coupling ($V$)
and the nonlocal EPC ($\Delta V$). The distinct transport behaviors with
respect to EPC are analyzed by carrier mobility, mean free path, optical
conductivity and one-particle spectral function. We have also identified an
"intermediate regime" where none of the established pictures applies, and the
generally perceived hopping regime is found to be at a very limited end in the
proposed general paradigm.
