Quantum Hall ice

We show that the chiral kagome ice manifold exhibits an anomalous integer quantum Hall effect (IQHE) when coupled to itinerant electrons. Although electron-mediated interactions select a magnetically ordered ground state, the full ice manifold can coexist with the IQHE over a range of finite temperatures. The degenerate ice states provide a natural realization of power-law correlated flux disorder, for which the spectral gap of the system remains robust. The quantized (up to exponentially small finite-temperature corrections) Hall conductance persists over a wide range of electron densities due to the disorder-induced localization of electronic states.