| We show that chiral kagome ice, an energetically stable manifold of Ising spins on kagome lattice, exhibits an anomalous quantum Hall effect when coupled to itinerant electrons. The highly degenerate ice states provide a natural realization of power-law correlated random fluxes. Remarkably, the spectral gap of this system is robust despite the strong disorder experienced by the electrons. The presence of correlated disorder also stabilizes the a quantized Hall conductance over a wide range of filling fractions due to localization of electron eigenstates. We further show that emergent monopoles, i.e. topological defects in this ice-like manifold, bind a fluctuating electric dipole. |
|