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 excited-state quantum phase transitions (ESQPT) in the Lipkin-Meshkov-Glick (LMG) model. We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of ESQPT. We further consider the diagonal entropy as a random variable over a certain time interval and focus on the statistical properties of the diagonal entropy. We find that the probability distribution of the diagonal entropy provides a clear distinction between different phases of ESQPT. In particular, we observe that at the critical point the probability distribution of the diagonal entropy has a universal form, which can be well described by the so-called beta distribution. We finally demonstrate the central moments of the diagonal entropy can reliably detect the critical point of ESQPT.

Work statistics and symmetry breaking in an excited-state quantum phase transition

“…Focussing on the LMG model we have demonstrated that while the average work, and higher moments of the distributions, are indifferent to either the presence of an ESQPT or the effect of symmetry breaking, the distribution itself is acutely sensitive to both. Furthermore, we have established that the entropy of the diagonal ensemble is a favourable figure of merit for pinpointing and studying ESQPTs and the symmetry breaking effects [39]. The qualitative features exhibited when the system is initialized in the ground state were shown to largely extend to initially excited states, with some notable changes, in particular, the emergence of a bimodal distribution for the work that is nevertheless sensitive to quenches to the ESQPT.…”

“…Such impact is also visible as a cusp in the work distribution, leading to complex survival probability dynamics [12]. Remarkably, the ESQPT yields critical signatures in other quantities, such as in out-of-time correlators [36], decoherence rates [17,18], or in phase-space quasi-probability distributions [37], and such signatures hold under different protocols, either under infinitesimal [38] or time-dependent quenches [39]. Yet, although second order QPTs and ESQPTs are intimately related to spontaneous symmetry breaking, the impact of such fundamental process in these dynamical quantities has so far been overlooked, with the notable exceptions in the realm of dynamical quantum phase transitions [40], where symmetry breaking upon a sudden quench is key for the emerging non-analytical behavior [19,[41][42][43][44][45][46].…”

Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis

“…Different kinds of ESQPTs have been identified, both theoretically [38][39][40][41][42][43][44] and experimentally [45][46][47], in various many body systems. These works have derived much efforts to look at the effects of ESQPTs on the nonequilibrium properties of quantum many body systems [48][49][50][51][52][53][54][55][56][57][58]. Such studies are in turn opened new avenues for detecting ESQPTs through the nonequilibrium quantum dynamics in many body systems [59][60][61][62], which can be accessed within current experimental technologies [63].…”