Existence of an intermediate interaction regime for highly mobile many-anyon clusters

Determine whether an intermediate regime exists in the anyon-Hubbard model with weak attractive on-site interactions, in which the kinetic binding mechanism stabilizes clusters of more than a few anyons while their effective tunneling remains sufficiently large that the clusters do not become heavy.

Background

The paper establishes kinematically bound two-, three-, and four-body clusters in the one-dimensional anyon-Hubbard model that remain highly mobile even at vanishing on-site interaction. It then discusses extending this mechanism to clusters containing more particles by adding weak attractive interactions.

The proposed regime must satisfy two competing requirements: the attraction should be strong enough to stabilize kinetic binding for larger clusters, but weak enough to prevent the effective tunneling amplitude from becoming exponentially small with particle number. The authors explicitly leave the existence of such a regime unresolved.