  Control of quantum coherence in many-body system is one of the key issues in
modern condensed matter. Conventional wisdom is that lattice vibration is an
innate source of decoherence, and amounts of research have been conducted to
eliminate lattice effects. Challenging this wisdom, here we show that lattice
vibration may not be a decoherence source but an impetus of a novel coherent
quantum many-body state. We demonstrate the possibility by studying the
transverse-field Ising model on a chain with renormalization group and
density-matrix renormalization group method, and theoretically discover a
stable $\mathcal{N}=1$ supersymmetric quantum criticality with central charge
$c=3/2$. Thus, we propose an Ising spin chain with strong spin-lattice coupling
as a candidate to observe supersymmetry. Generic precursor conditions of novel
quantum criticality are obtained by generalizing the Larkin-Pikin criterion of
thermal transitions. Our work provides a new perspective that lattice vibration
may be a knob for exotic quantum many-body states.
