Anyon-Impurity Bound States in Quantum-Engineered Fractional Chern Insulators

This study investigates whether a mobile impurity particle can be bound to a pinned quasihole—a topological excitation—within a fractional Chern insulator (FCI). The authors aim to determine if this 'anyon-impurity' composite is stable in quantum-engineered lattice systems, such as cold-atom platforms, and whether this binding can be used to measure the fractional charge of the quasihole or to manipulate anyons for future quantum information protocols.

The researchers employ a combination of analytical modeling and large-scale numerical simulations. They model the system using the interacting Harper-Hofstadter Hamiltonian, which supports Laughlin-type FCI ground states. By introducing a localized pinning potential, they create a quasihole and study its interaction with a mobile impurity. They use Density Matrix Renormalization Group (DMRG) and Matrix Product State (MPS) methods to calculate the binding energy and spatial structure of the composite object across different interaction strengths and system geometries.

The study establishes that a mobile impurity effectively binds to a quasihole in the FCI regime. The binding energy is found to be directly proportional to the fractional charge of the quasihole, particularly in the weak-coupling limit. This provides a practical, experimentally feasible protocol for measuring fractional charges in cold-atom experiments. Furthermore, the authors demonstrate that the anyon-impurity composite can be coherently transported by dynamically steering the external pinning potential, suggesting a viable path toward controlled braiding of anyons in the bulk of quantum-engineered materials.