  The speed limit of information propagation is one of the most fundamental
features in non-equilibrium physics. The region of information propagation by
finite-time dynamics is approximately restricted inside the effective light
cone that is formulated by the Lieb-Robinson bound. To date, extensive studies
have been conducted to identify the shape of effective light cones in most
experimentally relevant many-body systems. However, the Lieb-Robinson bound in
the interacting boson systems, one of the most ubiquitous quantum systems in
nature, has remained a critical open problem for a long time. This study
reveals a tight effective light cone to limit the information propagation in
interacting bosons, where the shape of the effective light cone depends on the
spatial dimension. To achieve it, we prove that the speed for bosons to clump
together is finite, which in turn leads to the error guarantee of the boson
number truncation at each site. Furthermore, we applied the method to provide a
provably efficient algorithm for simulating the interacting boson systems. The
results of this study settle the notoriously challenging problem and provide
the foundation for elucidating the complexity of many-body boson systems.
