Cluster dynamics in two-dimensional lattice gases with intersite interactions

Sufficiently strong intersite 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 intersite 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 multiple timescales. Although this is generally true, it is especially relevant in some lattices, including triangular and diamond lattices for hard-core bosons, and square lattices for soft-core bosons, where dimers move resonantly in either a kagome or a Lieb lattice. As a result, dimers show two very different transport velocities-a fast one comparable to the motion of individual particles, and a very slow one associated to flatband quasilocalization. Moreover, these lattices permit the resonant motion of longer clusters, and, remarkably, trimers move faster than quasi-flatband dimers for sufficiently strong optical lattices. This rich interplay between multiscaled quantum walk dynamics, quasilocalization, and flatband physics may be readily observed in experiments with lanthanide atoms.