  Bound states in the continuum (BICs) are localized modes residing in the
radiation continuum. They were first predicted for single-particle states, and
became a general feature of many wave systems. In many-body quantum physics, it
is still unclear what would be a close analog of BICs, and whether
interparticle interaction may induce BICs. Here, we predict a novel type of
multiparticle states in the interaction-modulated Bose-Hubbard model that can
be associated with the BIC concept. Under periodic boundary conditions, a
so-called quasi-BIC appears as a bounded pair residing in a standing wave
formed by the third particle. Under open boundary conditions, such a hybrid
state becomes an eigenstate of the system. We demonstrate that the Thouless
pumping of the quasi-BICs can be realized by modulating the on-site
interactions in space and time. Surprisingly, while the center-of-mass of the
quasi-BIC is shifted by a unit cell in one cycle, the bounded pair moves into
the opposite direction with the standing wave.
