Bosonic continuum theory of one-dimensional lattice anyons

Recent experimental advances in ultracold atomic gases have opened a route towards one-dimensional abelian anyons via bosons with an occupation-dependent hopping. Thereby, tunable two-particle interactions take over the role of intricate topological quantum mechanical constraints. Yet, this method crucially depends on the existence of a discrete lattice. A corresponding anyonic continuum theory that obeys the necessary periodicity in the anyonic phase angle is unknown. In this talk, we provide the continuum limit of one-dimensional lattice anyons and its representation by one-dimensional bosons. The theory maintains the periodicity in the anyonic phase and includes current density as well as three-body interactions. In the limit of a small anyonic phase, the integrable Kundu model is recovered. Here, our analysis provides a physical explanation of controversially discussed divergences. The results show how one-dimensional anyons in the continuum are experimentally accessible in purely bosonic systems.