  In two-dimensional hybrid organic-inorganic metal-halide perovskites, the
intrinsic optical lineshape reflects multiple excitons with distinct binding
energies, each dressed differently by the hybrid lattice. Given this
complexity, a fundamentally far-reaching issue is how Coulomb-mediated
many-body interactions --- elastic scattering such as excitation-induced
dephasing, inelastic exciton bimolecular scattering, and multi-exciton binding
--- depend upon the specific exciton-lattice coupling. We report the intrinsic
and density-dependent exciton pure dephasing rates and their dependence on
temperature by means of a coherent nonlinear spectroscopy. We find
exceptionally strong screening effects on multi-exciton scattering relative to
other two-dimensional single-atomic-layer semiconductors. Importantly, the
exciton-density dependence of the dephasing rates is markedly different for
distinct excitons. These findings establish the consequences of particular
lattice dressing on exciton many-body quantum dynamics, which critically define
fundamental optical properties that underpin photonics and quantum
optoelectronics in relevant exciton density regimes.
