Emergent gauge fields in band insulators.

By explicit microscopic construction involving a mapping to a quantum vertex model subject to the "ice rule," we show that an electronically "trivial" band insulator with suitable vibrational (phonon) degrees of freedom can host a "resonating valence-bond" state-a quantum phase with emergent gauge fields. This type of band insulator is identifiable by the existence of emergent gapless "photon" modes and deconfined excitations, the latter of which carry nonquantized mobile charges. We suggest that such phases may exist in the quantum regimes of various nearly ferroelectric materials.