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Condensed matter physics, area laws & LQG?

  1. Dec 11, 2017 #381

    atyy

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    https://arxiv.org/abs/1712.02803
    Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
    ChunJun Cao, Sean M. Carroll
    (Submitted on 7 Dec 2017)
    We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how Radon transforms can be used to convert this data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.
     
  2. Jan 17, 2018 #382

    atyy

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    https://arxiv.org/abs/1711.10854
    A Review of the Holographic Relation between Linearized Gravity and the First Law of Entanglement Entropy
    Rasmus Jaksland
    (Submitted on 29 Nov 2017)
    This thesis reviews the conjectured holographic relation between entanglement and gravity due to Mark van Raamsdonk and collaborators. It is accounted how the linearized Einstein equations both with and without matter in a d+1-dimensional AdS background can be derived from the first law of entanglement entropy in a d-dimensional CFT. This derivation builds on the Ryu-Takayanagi formula that relates entanglement entropy for CFT subsystems to extremal surfaces in the AdS bulk. The relation between gravity and entanglement is also corroborated by a qualitative investigation of the duality between the thermofield double state and the maximally extended AdS/Schwarzschild black hole using the Bekenstein-Hawking formula. Furthermore, this qualitative argument is generalized to generic CFT states with a classical spacetime dual using the Ryu-Takayanagi. The thesis also reviews the most relevant prerequisites for this holographic relation between gravity and entanglement: Anti-de Sitter spacetime, entanglement and entanglement entropy, gauge/gravity duality, the Ryu-Takayanagi formula, and linearized gravity.

    https://arxiv.org/abs/1801.05289
    Space-time random tensor networks and holographic duality
    Xiao-Liang Qi, Zhao Yang
    (Submitted on 16 Jan 2018)
    In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the Renyi entropies satisfying the covariant Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local reconstruction properties. We also investigate the unitarity of boundary theory in spacetime geometries with Lorenzian signature. Compared with the spatial random tensor networks, the space-time generalization does not require a particular time slicing, and provides a more covariant family of microscopic models that may help us to understand holographic duality.
     
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