Tunable Statistics-Induced Caging in the Anyon-Hubbard Model

Anyons exhibit fractional exchange statistics that interpolate between standard bosons and fermions, governing unique quantum interference phenomena in lattices. In discrete geometric units like a four-site plaquette, synthetic gauge fields can induce destructive quantum interference that traps particles, a phenomenon known as Aharonov-Bohm (AB) caging. While single-particle caging is robust, many-body AB caging is notoriously fragile against weak interparticle interactions because scattering processes disrupt the necessary interference conditions. This paper investigates whether the intrinsic anyonic statistical phase alone can induce AB caging for two interacting anyons, and whether an external high-frequency time-periodic drive can coherently control this caging to realize localization for arbitrary statistical parameters across different interaction regimes.

The authors examine the Anyon-Hubbard model on a diamond-shaped four-site plaquette for a two-particle sector. Using a fractional Jordan-Wigner transformation, the anyonic model is mapped exactly to an equivalent bosonic Hamiltonian with twisted boundary conditions, which is subsequently converted into a translationally invariant form via a local gauge transformation. In the undriven and weakly interacting regime, target-site occupation probabilities exhibit ongoing oscillations, indicating complete absence of caging. However, in the strongly interacting limit, the energy spectrum splits into a lower scattering manifold and an upper band of bound doublon states. Second-order degenerate perturbation theory reveals that doublon tunneling acquires an effective statistical phase, leading to exact destructive interference and static AB caging precisely when the statistical parameter equals one-half.

To overcome the limitations of undriven caging in the weakly interacting regime, the system is subjected to a two-dimensional high-frequency external driving field combined with static energy detunings. This periodic driving implements photon-assisted tunneling that renormalizes the effective hopping matrix elements. By tuning the synthetic Floquet flux alongside the anyonic statistical phase, the caging effect is successfully extended into the weakly interacting regime across all values of the statistical parameter. Furthermore, adjusting the polarization angle of the driving field permits selective caging, offering an efficient scheme for manipulating anyons and experimentally identifying their statistical phases.