Diagnosing excited state quantum phase transition with multiple quantum coherence spectrum in the Lipkin-Meshkov-Glick model
We use the multiple quantum coherence (MQC) spectrum to explore the effect of excited-state quantum phase transition (ESQPT) on the quantum coherence in the Lipkin-Meshkov-Glick (LMG) model--a paradigmatic model in the studies of ESQPTs. MQC spectrum is calculated with respect to a given reference basis and applied to both evolved and long time averaged states. We show that the MQC spectrum undergoes an abrupt change as the system passes through ESQPT, indicating a strong impact of ESQPT on quantum coherences. We further discuss the ability of zero mode of MQC spectrum to probe the presence of ESQPT and verify that it behaves as a realiable indicator of ESQPT. In addition, we perform an investigation on the behavior of MQC spectrum width. We find that the MQC spectrum widths for the evolved and long time averaged states are act as good ESQPT witnesses. Our results provide further evidence to confirm the usefulness of the MQC spectrum for diagnosing different types of phase transitions in many-body quantum systems.