Cluster dynamics in two-dimensional lattice gases with inter-site interactions

TL;DR

This paper explores the complex dynamics of inter-site bound clusters in two-dimensional lattice gases, revealing unique behaviors such as multi-scale quantum walks and partial localization linked to flat-band physics, with implications for experimental observation.

Contribution

It uncovers the rich and distinct dynamics of inter-site clusters in 2D lattices, highlighting their resonance with flat-band phenomena and differences from on-site cluster behavior.

Findings

Dimers perform multi-scale quantum walks on different lattice geometries.

Partial quasi-localization occurs due to flat-band effects.

Dynamics are especially notable in triangular and diamond lattices.

Abstract

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.