Operator entanglement entropy of the time evolution operator in chaotic systems

Zhou, Tianci; Luitz, David J.

doi:10.1103/physrevb.95.094206

Cited by 103 publications

(98 citation statements)

References 73 publications

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“…The entanglement measures of unitary time evolution operators capture the delocalization of information in quantum systems, and have been studied as an information-theoretic probe of chaotic dynamics in a variety of quantum systems [11,[22][23][24][25][26][27][28][29]. Here we briefly review the construction of operator entanglement measures, in particular the bi-and tri-partite operator mutual information.…”

Section: Operator Entanglementmentioning

confidence: 99%

“…It is further illuminating to understand the operator entanglement for holographic theories and its phase transitions in terms of the torus partition function. Luckily, the cross-ratios (26) are always real and between 0 and 1, so the only possible dominant saddles are the familiar thermal AdS and BTZ black hole. Interestingly, we find that the Thermal AdS partition function reproduces only the quasi-particle picture…”

Section: Tomimentioning

confidence: 99%

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Conformal field theory and the web of quantum chaos diagnostics

Kudler-Flam

Nie

Ryu

2020

J. High Energ. Phys.

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We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from "large-N" limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.

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Section: Operator Entanglementmentioning

confidence: 99%

Section: Tomimentioning

confidence: 99%

Conformal field theory and the web of quantum chaos diagnostics

Kudler-Flam

Nie

Ryu

2020

J. High Energ. Phys.

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“…Unfortunately, very few explicit results are available for realistic systems, although calculations in conformal field theories (CFTs) with large central charge [4][5][6][7], holographic setups [8], and mean-field-like models [9] provide useful insights. Several tools have been proposed to diagnose scrambling, such as the tripartite information [10][11][12][13], out-of-time-order correlators [3,[14][15][16][17][18], and entanglement of operators [19][20][21][22][23][24][25][26][27][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Quantum information scrambling after a quantum quench

Alba

Calabrese

2019

Phys. Rev. B

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How quantum information is scrambled in the global degrees of freedom of non-equilibrium manybody systems is a key question to understand local thermalization. A consequence of scrambling is that in the scaling limit the mutual information information between two intervals vanishes at all times, i.e., it does not exhibit a peak at intermediate times.Here we investigate the mutual information scrambling after a quantum quench in both integrable and non-integrable one dimensional systems. We study the mutual information between two intervals of finite length as a function of their distance. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signalling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading. In the scaling limit of large intervals, times, and distances between the intervals, with their ratios fixed, this predicts a decay exponent equal to 1/2. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For non-integrable models, a much faster decay is observed, which can be attributed to the finite life time of the quasiparticles: unsurprisingly, non-integrable models are better scramblers. arXiv:1903.09176v2 [cond-mat.stat-mech]

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“…In this section, we provide a technical discussion pertinent to the concepts of the entanglement entropy of both quantum wave functions |ψ and quantum evolution op-eratorsÛ for the case of a complementary real-space bipartition in terms of two subsystems A and B ≡ A, with a tensor product Hilbert space H = H A ⊗H B . For a more detailed discussion we refer the reader to [40,42,43].…”

Section: Wave Function and Operator Entanglement Entropymentioning

confidence: 99%

“…In Refs. [42][43][44], this concept was directly applied to the time evolution operator U (t), and a generic linear growth of the operator entanglement entropy (opEE) in ergodic quantum systems was found, while MBL systems are characterized by a logarithmic growth in time [42].…”

Section: Introductionmentioning

confidence: 99%

Power-law entanglement growth from typical product states

Lezama

Luitz

2019

Phys. Rev. Research

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Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy.Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states with the operator entanglement entropy of the unitary evolution operator, while special product states, e.g. σz basis states, can exhibit faster entanglement production.In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorderdependent exponent, and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition. arXiv:1908.07010v1 [cond-mat.dis-nn]

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Operator entanglement entropy of the time evolution operator in chaotic systems

Cited by 103 publications

References 73 publications

Conformal field theory and the web of quantum chaos diagnostics

Conformal field theory and the web of quantum chaos diagnostics

Quantum information scrambling after a quantum quench

Power-law entanglement growth from typical product states

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