Anyonic topological flat bands

Topological flat bands have attracted significant interest across various branches of physics, where synthetic gauge fields are typically considered an essential prerequisite. Numerous mechanisms have been proposed for implementing these fields, including magnetic fields on electrons, differential optical paths for photons, and strain-induced effective magnetic fields, among others. In this work, we introduce a novel approach to generating synthetic gauge fields through quantum statistics and demonstrate their effectiveness in realizing anyonic topological flat bands. Notably, we discover that a pair of strongly interacting anyons can induce square-root topological flat bands within a lattice model that remains dispersive and topologically trivial for a single particle. To validate our theoretical predictions, we experimentally simulate the quantum statistics-induced topological flat bands and square-root topological boundary states by mapping the eigenstates of two anyons onto modes in electric circuits. Our findings not only open a new pathway for creating topological flat bands but also deepen our understanding of anyonic physics and the underlying principles of flat-band topology.