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Halpern, Joshua B.; Nathans, R.; Yergin, P.F.

doi:10.1103/physrev.95.1529

Cited by 14 publications

(6 citation statements)

References 5 publications

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“…The 2-REE has been observed in a recent experiment with ultracold atoms [101,102]. There are also several proposals of measuring OTOCs [103][104][105], and OTOCs have been indeed measured with trapped ions [106]. Furthermore, unitary designs are experimentally realized with nuclear magnetic resonance systems [107,108].…”

Section: Summary and Discussionmentioning

confidence: 99%

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

2020

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Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order complexity, which is represented by the eigenstate thermalization hypothesis (ETH) stating that individual energy eigenstates are thermal. Here, we propose a higher-order generalization of the ETH, named the k-ETH (k = 1, 2, . . . ), to quantify higher-order complexity of quantum many-body dynamics at the level of individual energy eigenstates, where the lowest order ETH (1-ETH) is the conventional ETH. The explicit condition of the k-ETH is obtained by comparing Hamiltonian dynamics with the Haar random unitary of the k-fold channel. As a non-trivial contribution of the higher-order ETH, we show that the k-ETH with k ≥ 2 implies a universal behavior of the kth Rényi entanglement entropy of individual energy eigenstates. In particular, the Page correction of the entanglement entropy originates from the higher-order ETH, while as is well known, the volume law can be accounted for by the 1-ETH. We numerically verify that the 2-ETH approximately holds for a nonintegrable system, but does not hold in the integrable case. To further investigate the information-theoretic feature behind the k-ETH, we introduce a concept named a partial unitary k-design (PU k-design), which is an approximation of the Haar random unitary up to the kth moment, where partial means that only a limited number of observables are accessible. The k-ETH is a special case of a PU k-design for the ensemble of Hamiltonian dynamics with random-time sampling. In addition, we discuss the relationship between the higher-order ETH and information scrambling quantified by out-of-time-ordered correlators. Our framework provides a unified view on thermalization, entanglement entropy, and unitary k-designs, leading to deeper characterization of higher-order quantum complexity. Contents

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Section: Summary and Discussionmentioning

confidence: 99%

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

2020

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“…The deep connection between OTOC and quantum chaos generated a lot of interest in the topic, both theoretically and experimentally. Several protocols have been proposed to measure these unconventional correlators in real experimental systems [30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Information scrambling in chaotic systems with dissipation

2019

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Chaotic dynamics in closed local quantum systems scrambles quantum information, which is manifested quantitatively in the decay of the out-of-time-ordered correlators (OTOC) of local operators. How is information scrambling affected when the system is coupled to the environment and suffers from dissipation? In this paper, we address this question by defining a dissipative version of OTOC and numerically study its behavior in a prototypical chaotic quantum chain in the presence of dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the 'information light cone' can only reach a finite distance even when the effect of overall decay is removed. Based on this observation we conjecture a modified version of the Lieb-Robinson bound in dissipative systems.

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“…The quantum simulation of scrambling with nearterm processors is especially challenging because, at each time t, four Hamiltonian simulations of length t are implemented to calculate F , two each moving forward and backward in time. In addition, F is complex so it has to be measured interferometrically [30][31][32], requiring extra qubits and gates, or via weak measurement [33], which is not widely available. It is also possible to measure scrambling via correlations between randomized measurements [18].…”

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confidence: 99%

Quantum simulation of operator spreading in the chaotic Ising model

Geller,

Arrasmith,

Holmes

et al. 2021

Preprint

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A40(γ, n)Threshold and the Mass ofA

Cited by 14 publications

References 5 publications

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization

Information scrambling in chaotic systems with dissipation

Quantum simulation of operator spreading in the chaotic Ising model

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