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

TL;DR

This paper demonstrates that the diagonal entropy's dynamical and statistical properties serve as effective indicators for excited-state quantum phase transitions in the Lipkin-Meshkov-Glick model, revealing universal distribution features at critical points.

Contribution

It introduces the use of diagonal entropy's dynamical evolution and probability distribution analysis as novel tools to characterize ESQPTs, highlighting universal behavior at criticality.

Findings

Diagonal entropy evolution signals ESQPT presence.

Probability distribution of diagonal entropy distinguishes phases.

Universal beta distribution at the ESQPT critical point.

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.