Tamm-Hubbard surface states in the continuum

In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential $V$ at the lattice boundary. Such thresholdless surface states, that can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential $V$ is attractive (repulsive) and the particle-particle Hubbard interaction $U$ is repulsive (attractive), i.e. for $UV<0$.