  We elucidate the relation between out-of-time-order correlators (OTOCs) and
quantum phase transitions via analytically studying the OTOC dynamics in a
degenerate spectrum. Our method points to key ingredients to dynamically detect
quantum phases via out-of-time-order correlators for a wide range of quantum
phase transitions and explains the existing numerical results in the
literature. We apply our method to a critical model, XXZ model that numerically
confirms our predictions.
