Information Scrambling and Loschmidt Echo

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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“…(5) The OTOC was equated with the thermally averaged Loschmidt echo in Ref. [13]. This was further explored in Ref.…”

Section: A Spectral Form Factormentioning

confidence: 99%

“…[17]. (13) The circuit complexity was suggested to be related to the logarithm of the Loschmidt echo in Ref. [6].…”

Section: A Spectral Form Factormentioning

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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“…Therefore, it is not surprising that the OTOCs may be extracted from echo spectroscopy as proposed in [27][28][29][30] and measured experimentally in [10]. More recently, the connection between the OTOC and the Loschmidt echo at infinite temperature was also explored in [31].…”

Section: Study Of the Otoc In Syk In The Limit Of Large Interaction Omentioning

confidence: 99%

Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?

Romero-Bermúdez

Schalm

Scopelliti

2019

J. High Energ. Phys.

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We study the contour dependence of the out-of-time-ordered correlation function (OTOC) both in weakly coupled field theory and in the Sachdev-Ye-Kitaev (SYK) model. We show that its value, including its Lyapunov spectrum, depends sensitively on the shape of the complex time contour in generic weakly coupled field theories. For gapless theories with no thermal mass, such as SYK, the Lyapunov spectrum turns out to be an exception; their Lyapunov spectra do not exhibit contour dependence, though the full OTOCs do. Our result puts into question which of the Lyapunov exponents computed from the exponential growth of the OTOC reflects the actual physical dynamics of the system. We argue that, in a weakly coupled Φ 4 theory, a kinetic theory argument indicates that the symmetric configuration of the time contour, namely the one for which the bound on chaos has been proven, has a proper interpretation in terms of dynamical chaos. Finally, we point out that a relation between these OTOCs and a quantity which may be measured experimentally -the Loschmidt echo -also suggests a symmetric contour configuration, with the subtlety that the inverse periodicity in Euclidean time is half the physical temperature. In this interpretation the chaos bound reads λ ≤ 2π β = πT physical .

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“…Note that it has been shown that the unregularized OTOC does not share the universal Lyapunov exponent with the regularized OTOC due to the sensitivity of the infrared regulator [14,15,16,17,18,19,20,21,22,23]. Further, protocols to measure the regularized OTOC have been given [24,25,26], applied to Jaynes-Cummings (JC) interactions [27,28] and the Loschmidt echo [29,30], and implemented [31,32] which confirms that λ is an experimental observable. Taken together, these facts establish the OTOC as a useful probe of quantum chaos.…”

Section: Introductionmentioning

confidence: 88%

Spectral form factor as an OTOC averaged over the Heisenberg group

Koch

Huang

et al. 2019

Physics Letters B

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We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field theory, there is an analogous result with the average taken over the tensor product of many copies of the Heisenberg group, one copy for each field mode. The resulting formula is expressed as a path integral over two fields, providing a promising approach to the computation of the spectral form factor. We develop the formula that we have obtained using a coherent state description from the JC model and also in the context of the large-N limit of CFT and Yang-Mills theory from the large-N matrix quantum mechanics.

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Information Scrambling and Loschmidt Echo

Cited by 140 publications

References 63 publications

Conformal field theory and the web of quantum chaos diagnostics

Conformal field theory and the web of quantum chaos diagnostics

Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?

Spectral form factor as an OTOC averaged over the Heisenberg group

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