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arXiv:2608.06233

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

Botao Wang, Amit Vashisht, Felix A. Palm, Fabian Grusdt, Laurens Vanderstraeten, Nathan Goldman

cond-mat.mes-hallcond-mat.quant-gascond-mat.str-elquant-phSubmitted Aug 6, 2026• Announced Aug 7, 2026• 0 citations
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Abstract

Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.

Comments
5.5+4 pages, 4+5 figures, comments are welcome!

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Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.
Coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in fractional Chern insulators. Our approach employs impurities with individually addressable internal states that bind to the anyons, allowing their adiabatic motion and exchange under full spatial control. By combining Ramsey and spin-echo sequences using one and two impurities, the protocol gives independent access to the Aharonov-Bohm and exchange contributions to the total geometric phase, thereby providing an unambiguous probe of anyonic statistics. Our scheme can potentially be implemented in cold-atom quantum simulators as well as in van der Waals heterostructures. Complementary finite-size simulations in non-interacting Chern insulators quantify the system sizes required to faithfully extract geometric phases, highlighting the role of edge effects. Our results establish impurity-based interferometry as a feasible route toward direct anyon braiding experiments in quantum simulators and lay the groundwork for future explorations of non-Abelian braiding and topological quantum control.
Immersing a mobile impurity in a quantum many-body environment can reveal fundamental properties of the background medium, hence providing a powerful probe of quantum matter. This approach is particularly intriguing when considering media with exotic properties, such as strongly-correlated phases and topological states of matter. In this work, we study the dressing of a mobile impurity interacting with a chiral mode, at the edge of topological quantum matter. The resulting “chiral polaron” is characterized by an asymmetric spectral function, which reflects the chirality and group velocity of the topological edge mode. We first build our theoretical understanding from an effective one-dimensional chiral model, which captures the hallmark signatures of chiral polaron. We then demonstrate how this simple picture extends to realistic models of integer and fractional Chern insulator states, by adapting tensor-network methods to polaron spectroscopy. Injecting mobile impurities on the edge of topological quantum matter is shown to be a powerful tool to probe exotic edge properties, particularly suitable for cold-atom experiments. Mobile impurities can be useful probes of quantum states. Here, the authors theoretically identify polarons formed on the edge of topological insulating states, termed chiral polarons, that can be used to probe topological matter.
We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally relevant open boundary conditions show that already a four-particle system exhibits signatures of charge fractionalization in the quantum-Hall-like state at the filling fraction of 1/21/21/2 particle per flux quantum. This result is favorable for the prospects of adiabatic preparation of fractional Chern insulators. Our work is inspired by recent experimental breakthroughs in atomic quantum gases: the realization of strong artificial magnetic fields in optical lattices, the ability of single-site addressing in quantum gas microscopes, and the preparation of low-entropy insulating states by engineering an entropy-absorbing metallic reservoir.
We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling nu = 1/2, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose, we employ a tree tensor network technique, which allows us to study systems with up to N = 18 particles on a 16 x 16 lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [E. Macaluso et al., Phys. Rev. Lett. 123, 266801 (2019)]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.
The question of anyon interactions and their possible binding plays a key role in the physics of fractional quantum Hall states. Here, we introduce a controlled and scalable approach to study anyon binding by working entirely within the Hilbert space of anyons. The resulting theory is characterized by an effective potential, which captures the electrostatic energy of classical anyon configurations, and a Kähler potential, which simultaneously encodes the anyon Berry phase and the structure of their Hilbert space; both quantities are readily computed using Monte Carlo methods for large systems, enabling reliable extrapolation to the thermodynamic limit. By applying the formalism of geometric quantization on Kähler manifolds, we construct the anyon Hamiltonian, which can be exactly diagonalized in the few-anyon Hilbert space. Applying our approach to the quasiholes of the ν=1/3ν=1/3ν=1/3 Laughlin state with screened Coulomb interaction, we find that Laughlin quasiholes form bound states for screening lengths comparable or smaller than the magnetic length. Remarkably, binding occurs despite both the bare electron-electron interaction and the quasihole electrostatic potential being purely repulsive. The bound-state formation is a Berry phase effect, driven by oscillations in the quasihole density profile on the ℓB\ell_BℓB​ scale that are invisible in the quasihole electrostatic potential alone. For multiple quasiholes, we identify a sequence of phases as the screening length is reduced: free e/3e/3e/3 anyons, paired 2e/32e/32e/3 bound states, three-anyon charge-eee clusters, and larger composite objects. Finally, we discuss possible signatures in charge imaging experiments on quantum Hall systems and the relevance to the phase diagram of itinerant anyon phases in fractional quantum anomalous Hall materials.
Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states, hosting topological order and fractionalized anyonic excitations. Their realization poses a demanding target for quantum simulation. Here, we realize a bosonic FCI on an IBM Nighthawk superconducting quantum processor using classically optimized variational circuits. We target a Laughlin-like state that is an exact zero-energy ground state of a long-range parent Hamiltonian on a torus, eliminating physical edges and providing a favorable geometry for accessing fractional quantum Hall physics in a small system. On a 4×44\times44×4 qubit lattice, we prepare both the four-boson FCI ground state and a three-boson state hosting two quasiholes. Measurements of particle densities and correlations reproduce the characteristic structure of the target states, while reconstructed chiral magnetization currents resolve the circulating current pattern associated with the quasiholes. The preparation of these strongly correlated topological states with shallow circuits establishes a route toward the digital simulation and manipulation of fractionalized excitations, including measurements of topological invariants and anyonic braiding.