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

Wang, Qian; Pérez‐Bernal, F.

doi:10.1103/physreve.103.032109

Cited by 18 publications

(12 citation statements)

References 71 publications

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“…They are somehow linked to thermal phase transitions [21,22] and dynamical phase transitions [23,24]. They can be identified by their consequences in the classical [25] and semiclassical [26,27] phase-space dynamics [28,29], as in the singularities of the density of states [30]. Its signatures have been theoretically and experimentally observed in several physical systems [31][32][33][34][35][36], and its connections with quantum Lyapunov exponents have been explored [37][38][39].…”

mentioning

confidence: 99%

Constant of Motion Identifying Excited-State Quantum Phases

Corps

Relaño

2021

Phys. Rev. Lett.

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We propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator Ĉ, which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues AE1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, Ĉ explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law.

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confidence: 99%

Constant of Motion Identifying Excited-State Quantum Phases

Corps

Relaño

2021

Phys. Rev. Lett.

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“…pinpointing and studying ESQPTs and the symmetry-breaking effects [38]. 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.…”

Section: Discussionmentioning

confidence: 97%

“…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 [35], decoherence rates [17,18], or in phase-space quasiprobability distributions [36], and such signatures hold under different protocols, either under infinitesimal [37] or time-dependent quenches [38]. 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 [39], where symmetry breaking upon a sudden quench is key for the emerging nonanalytical behavior [19,[40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

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“…To quantify the distance between P(x) and P 2 (x), we use two different deviation measures, namely the square root of the Kullback-Leibler divergence (SKLD) [123,124] and the root-mean-square error (RMSE) [125,126]. For the observed distribution P(x) and predicted distribution P ν (x), the SKLD (RMSE), denoted as D…”

Section: Multifractality Of Coherent Statesmentioning

confidence: 99%

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

Wang

Robnik

2021

Entropy

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We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

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

Cited by 18 publications

References 71 publications

Constant of Motion Identifying Excited-State Quantum Phases

Constant of Motion Identifying Excited-State Quantum Phases

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

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

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