Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy

Abstract: Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick (LMG) 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 further consider the diagonal entropy as a random variable over a certain time interval and we find that its associated probability distribution provides a clear distinction between the different phases of ESQPT. We observe that the probability distribution of the diagonal entropy at the ESQPT critical point has an universal form, well described by a beta distribution, and we demonstrate that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.