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

We elucidate the relation between out-of-time-order correlators (OTOCs) and phase transitions via analytically studying the OTOC dynamics both in non-degenerate and degenerate spectra. Our method indicates that for a wide variety of quantum phase transitions, OTOCs can directly characterize various quantum phases as well as their symmetry breaking patterns. Key ingredients about how to utilize OTOC to detect and characterize a quantum phase transition are presented. We further discuss how our method could be useful to understand the dynamical features of the OTOCs.