  Sufficiently strong inter-site interactions in extended-Hubbard and XXZ spin
models result in dynamically-bound clusters at neighboring sites. We show that
the dynamics of these clusters in two-dimensional lattices is remarkably
different and richer than that of repulsively-bound on-site clusters in gases
without inter-site interactions. Whereas on-site pairs move in the same lattice
as individual particles, nearest-neighbor dimers perform an interacting quantum
walk in a different lattice geometry, leading to a peculiar dynamics
characterized by more than one time scale. The latter is general for any
lattice geometry, but it is especially relevant in triangular and diamond
lattices, where dimers move resonantly in an effective kagome and Lieb lattice,
respectively. As a result, dimers experience partial quasi-localization due to
an effective flat band, and may move slower than longer clusters. This
surprising link between anomalously slow quantum walk dynamics in these models
and flat-band physics may be readily observed in experiments with lanthanide
atoms.
