Out-of-time ordered correlators, complexity, and entropy in bipartite systems

Bergamasco, Pablo D.; Carlo, Gabriel G.; Rivas, Alejandro Mariano Fidel

doi:10.1103/physrevresearch.1.033044

Cited by 26 publications

(17 citation statements)

References 27 publications

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“…See[19] for the OTOC analysis for the Henon-Heiles system. Various kinds of OTOCs in quantum maps were also studied[20][21][22][23]. The cases with large N are found in[24][25][26][27][28][29][30][31][32][33][34][35].…”

mentioning

confidence: 99%

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

J. High Energ. Phys.

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We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

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mentioning

confidence: 99%

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Hashimoto

Huh

Kim

et al. 2020

J. High Energ. Phys.

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“…Among all detectors of quantum chaos, we focus on spectral form factor (SFF) and out-of-time-ordered correlators (OTOCs). Both of them have been extensively used in numerous recent studies [18][19][20][21][22][100][101][102][103][127][128][129][130][131][132][133][134].…”

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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“…In the traditional approach, which has mainly focused on short-range correlations in the spectrum, level statistics and universal spectral properties through random matrix theory (RMT) [12][13][14] have been popular objects of study. However other indicators of chaos, such as the out-of-time order correlators (OTOC) [15][16][17] and the spectral form factor (SFF) [18], are also of interest. For example, they have been used to understand chaos in the Sachdev-Ye-Kitaev (SYK) model which is important in the context of black hole physics [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

2021

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We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of noninteracting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phasetransition point evolves in three time intervals. We make a systematic study of the emergence of these three timescales for various initial states and find that the number of time intervals remains 3 unless the Hamiltonian is tuned in the localized phase or when the initial state is maximally entangled, when there is a featureless time evolution. We find a broad direct correlation between the entanglement entropy and the length of the ramp of the SFF. We also find that in the delocalized phase the spectral correlations are stronger in the center of the spectrum and grow progressively weaker as more and more of the spectrum is considered.

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Out-of-time ordered correlators, complexity, and entropy in bipartite systems

Cited by 26 publications

References 27 publications

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

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

Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

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