Localized shocks

By Daniel A. Roberts, D. Stanford, L. Susskind. 2014

651 citations recorded by the source corpus.

A bstractWe study products of precursors of spatially local operators, Wxntn⋅⋅⋅Wx1t1$$ {W_x}_{{}_n}(tn)\cdot \cdot \cdot {W}_{x_1}\left({t}_1\right) $$, where Wx(t) = e− iHtWxeiHt. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in t. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/229d89352d85f9916ebb8658cdf1d9244ed34b40

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Citations in the corpus

Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “ide of the TFD.26 This growth saturates eq. (4.13) with v ent >v but in d>3 so one might worry that entanglement is spreading faster than the speed v but permitted by operator commutator growth [104]. Specically, by applying an analysis similar to the one reviewed around eq. (4.17) to thermal ”
Krylov complexity in saddle-dominated scrambling (2022, background): “A simple operator can become extremely complicated depending upon the nature of the Hamiltonian, and the given initial operator [37].”
Quantum entanglement of localized excited states at finite temperature (2014, neutral): “A related problem has been studied in the intriguing papers [9, 10].”
Entanglement is not enough (2014, background): “Roberts, Stanford, and I [7, 9] have devoted several papers to confirming the following proposition: The geometry of the minimal tensor network (equivalently the minimal quantum circuit) matches the Einstein geometry of the ERB in a coarse grained sense, with a spatial resolution of l, or in the Sch”
Chaos in quantum channels (2015, methodology): “In [38] and [5], this proposal was explored in a larger variety of black hole states that were perturbed by shock waves.”
Operator Spreading in Random Unitary Circuits (2017, methodology): “At time t, we may write the operator in the basis of products of Pauli matrices [11,22,23,58,82],”
Quantum complexity and negative curvature (2016, background): “In particular, this functional form will be true if we use ERB volume [1, 3] or action [12, 13].”
Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits (2019, background): “We expect this picture to hold true for more general, non-dual unitary, chaotic systems if one replaces the light cone spreading at the maximal speed (1 in our units) with an effective one spreading at the “butterfly velocity" vB [6] of the system.”
Disentangling Scrambling and Decoherence via Quantum Teleportation (2018, background): “While a precise definition of quantum scrambling remains elusive, a powerful proxy for characterizing its behavior is provided by out-of-time-order correlation (OTOC) functions, which take the general form hVð0ÞWðtÞVð0ÞWðtÞi, where V, W are operators that act on sufficiently small subsystems [8,10,1”
Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, methodology): “Some representative examples of such systems include (i) models that are (or are thought to be) holographically dual to black holes[19, 21, 22], including the Sachdev-Ye-Kitaev (SYK) model[24, 25] and chains of coupled SYK dots at large N [29], (ii) large-N gauge”
Krylov complexity in conformal field theory (2021, background): “[7] Daniel A Roberts, Douglas Stanford, and Leonard Susskind, “Localized shocks,” Journal of High Energy Physics 2015, 51 (2015).”