Anyonic bound states in the continuum

Bound states in the continuum (BICs), which are spatially localized states with energies lying in the continuum of radiating modes, are discovered both in single- and few-body systems with suitably engineered spatial potentials and particle interactions. Here, we reveal a type of BICs that appear in anyonic systems. It is found that a pair of non-interacting anyons can perfectly concentrate on the boundary of a one-dimensional homogeneous lattice when the statistical angle is beyond a threshold. Such a bound state is embedded into the continuum of two-anyon scattering states, and is called as anyonic BICs. In contrast to conventional BICs, our proposed anyonic BICs purely stem from the statistics-induced correlations of two anyons, and do not need to engineer defect potentials or particle interactions. Furthermore, by mapping eigenstates of two anyons to modes of designed circuit networks, the anyonic BICs are experimentally simulated by measuring spatial impedance distributions and associated frequency responses. Our results enrich the understanding of anyons and BICs, and can inspire future studies on exploring correlated BICs with other mechanisms. Bound states in the continuum (BIC) are localized waves confined in an open system and are a general wave phenomenon relevant to a range of systems from classical to quantum mechanics. Here, the authors propose BIC based on anyon statistics and confirm their model using electronic circuits.