Identifying excited-state quantum phase transition in a spinor Bose–Einstein condensate with out-of-time-order correlators

Out-of-Time-Order Correlator (OTOC) provides a way of quantifying information scrambling in quantum many-body systems and receives increasing attention from different fields. We extend the application of the OTOC to probe the excited-state quantum phase transitions (ESQPT) in spinor Bose–Einstein condensate in an external magnetic field. Using the quantum approach, mean-field theory, and numerical simulations, we have obtained the phase transition points and dynamical properties around them, and have demonstrated that these features can be detected by the OTOC. Our further investigations reveal that the detection efficiency is guaranteed under different magnetization conditions. Our results provide theoretical suggestions for using the OTOCs for experimentally accessing ESQPT in spinor quantum gases and other quantum many-body systems. • Extend the application of the OTOC to identify the excited-state quantum phase transitions (ESQPT) in spinor Bose–Einstein condensate. • Reveal that the detection efficiency is guaranteed under different magnetization conditions. • Provide theoretical suggestions for using the OTOCs for experimentally accessing ESQPT in spinor quantum gases and other quantum many-body systems.