  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 $UV<0$.
