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.

Automated summary

In models with sufficiently strong intersite interactions, clusters formed at neighboring sites exhibit distinct and rich dynamics on two-dimensional lattices compared to repulsively bound clusters in gases without intersite interactions. This results in a peculiar dynamics characterized by multiple timescales, especially in specific lattice structures like triangular, diamond, and square lattices for different types of bosons, where dimers can move resonantly in different lattice geometries.