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

We elucidate the relation between out-of-time-order correlators (OTOCs) and the phase transitions via analytically studying the OTOC dynamics both in non-degenerate and degenerate spectra. Our method points to key ingredients to dynamically detect quantum phases as well as their symmetry breaking patterns via out-of-time-order correlators for a wide range of quantum phase transitions. We apply our method to a critical model, XXZ model that numerically confirms our predictions. We further discuss how our method could be useful to understand the dynamical features of the OTOCs.