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 an optimal 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.

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