Detection of quantum phases via out-of-time-order correlators

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.