Characterizing the Lipkin-Meshkov-Glick model excited-state quantum phase transition using dynamical and statistical properties of the diagonal entropy

Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.

Automated summary

Using diagonal entropy, efficient indicators of the presence of ESQPT in the Lipkin-Meshkov-Glick model were identified through time evolution analysis. The probability distribution of diagonal entropy values over a certain time interval distinguished clearly between different phases of ESQPT, with a universal form observed at the critical point, described by a beta distribution. Reliable detection of ESQPT was found to be obtainable from central moments of the diagonal entropy.