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 novel type of band insulator is identifiable by the existence of emergent gapless `photon' modes and deconfined excitations, the latter of which carry non-quantized mobile charges. We suggest that such phases may exist in the quantum regimes of various nearly ferroelectric materials.