  In this work, we investigate effects of weak interactions on a bosonic
complete flat-band system. By employing a band projection method, the flat-band
Hamiltonian with weak interactions is mapped to an effective Hamiltonian. The
effective Hamiltonian indicates that doublons behave as well-defined
quasi-particles, which acquire itinerancy through the hopping induced by
interactions. When we focus on a two-particle system, from the effective
Hamiltonian, an effective subspace spanned only by doublon bases emerges. The
effective subspace induces spreading of a single doublon and we find an
interesting property: The dynamics of a single doublon keeps short-range
density-density correlation in sharp contrast to a conventional two-particle
spreading. Furthermore, when introducing a modulated weak interaction, we find
an interaction induced topological subspace embedded in the full Hilbert space.
We elucidate the embedded topological subspace by observing the dynamics of a
single doublon, and show that the embedded topological subspace possesses a
bulk topological invariant. We further expect that for the system with open
boundary the embedded topological subspace has an interaction induced
topological edge mode described by the doublon. The bulk--edge--correspondence
holds even for the embedded topological subspace.
