Bound states in the continuum (BICs), spatially localized states embedded in radiating continuum, have been extensively investigated in single-particle systems, also enabling high-performance applications in classical wave systems. Recently, exploring many-body BICs in correlated systems has emerged as a pivotal frontier with increasing research interest. However, the majority of previous studies focus largely on on-site interactions with tailored conditions, incurring significant implementation challenges. Whether off-site interactions, e.g., many-body hoppings, can generate many-body BICs and how to characterize them in experiments remains an open question. Here, we first predict and realize a boundary-localized two-body BIC, the bound pair state in the continuum (BPIC), arising from uniform two-body hoppings. Analytically, we demonstrate not just the formation of bound pairs, but the spectral coexistence of the boundary-localized BPIC and the scattering continuum. Experimentally, developing a phononic crystal platform as a classical-wave simulator, we map the correlated particle dynamics onto acoustic wave propagation and observe the acoustic BPIC. Our findings build a new bridge between the BIC research and many-body physics, and may promote the development of high-$Q$ acoustic devices in applications.

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• Bound states in the continuum
• Few-body systems
• Phononic crystals
• Quantum many-body systems