Abstract
We study products of precursors of spatially local operators, \( {W_x}_{{}_n}(tn)\cdot \cdot \cdot {W}_{x_1}\left({t}_1\right) \), where W x (t) = e − iHt W x e iHt. 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.
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Roberts, D.A., Stanford, D. & Susskind, L. Localized shocks. J. High Energ. Phys. 2015, 51 (2015). https://doi.org/10.1007/JHEP03(2015)051
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DOI: https://doi.org/10.1007/JHEP03(2015)051