Effective Non-Local Four-Body Interactions in 1D: Quantum Anomalies, Topological Defects, and Few-Body Correlations

We describe the physics generated by a novel four-body interaction of particles confined to one dimension. The interaction has a number of interesting features. First, it provides an effective theory for dynamically controlled long-range interactions between pairs of pairs of interacting particles. Second, in the strong positive coupling (repulsive) limit, the interaction creates a topological defect in the system's configuration space that can be exploited to generate anionic exchange statistics. Third, the interaction generates a quantum scaling anomaly, in a way similar to that for two-body interactions in two dimensions and three-body interactions in one dimension; we also describe how the breaking of the scale symmetry can be probed by controlling the confining-trapping potential. Fourth, in the strong negative coupling (attractive) limit, the interaction leads to strongly correlated states. These states exhibit intriguing properties, including the possibility of stabilization via competition between effective three- and four-body interactions. Finally, we discuss preliminary ideas and challenges for implementing these models with ultracold atoms.