  The propagation of excitons in TMD monolayers has been intensively studied
revealing interesting many-particle effects, such as halo formation and
non-classical diffusion. Initial studies have investigated how exciton
transport changes in twisted TMD bilayers, including Coulomb repulsion and
Hubbard-like exciton hopping. In this work, we investigate the
twist-angle-dependent transition of the hopping regime to the dispersive regime
of effectively free excitons. Based on a microscopic approach for excitons in
the presence of a moir\'e potential, we show that the hopping regime occurs up
to an angle of approximately 2{\deg} and is well described by the Hubbard
model. At large angles, however, the Hubbard model fails due to increasingly
delocalized exciton states. Here, the quantum mechanical dispersion of free
particles with an effective mass determines the propagation of excitons.
Overall, our work provides microscopic insights into the character of exciton
propagation in twisted van der Waals heterostructures.
