Constructing holographic spacetimes using entanglement renormalization
By Brian Swingle. 2012
238 citations recorded by the source corpus.
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large N limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large N limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large N theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bf084262081418ec7e0209b05d8bedb798c29926
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Citations in the corpus
- Cool horizons for entangled black holes (2013, background): “This pattern is reminiscent of hyperbolic space [38].”
- Complexity of formation in holography (2016, background): “One suggestion [61, 62] was to replace the bridge layer with trivial identity tensors, raising the temperature to infinity and eliminating the spatial correlations altogether — see also [63].”
- Chaos and complexity by design (2016, background): “75 [78] B. Swingle, “Entanglement Renormalization and Holography,” Phys.”
- Holographic local quenches and entanglement density (2013, background): “Indeed, it has been conjectured in [40] that the geometry described by a tensor network of a quantum critical system in MERA describes the AdS spacetime dual to this critical point.”
- Circuit complexity in quantum field theory (2017, background): “The AdS/MERA correspondence was the first proposal for a novel connection between holography and tensor networks [63, 64].”
- Surface/State Correspondence as a Generalized Holography (2015, unknown): “[7, 8, 9, 10, 11, 12, 13] for more”
- Bulk curves from boundary data in holography (2013, background): “Therefore, given the relation between geometry and entanglement discovered in [6] and studied in [7, 8, 9, 10, 11, 12, 13, 14], it would be natural to guess that areas of radial surfaces in AdS space are related to some sort of UV/IR entanglement in the dual field theory [20].”
- Entanglement is not enough (2014, background): “Tensor networks are thought of as existing in bulk space–at a fixed instant which represent the state at that time [14, 18, 19].”
- Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “(81) 5 After the preprint of this paper appeared on the arXiv, we noticed the preprint [45], where interesting behaviors in the large N limit of MERA were discussed.”
- Entwinement and the emergence of spacetime (2014, unknown): “The relevance of boundary entanglement for such a reconstruction was first pointed out in [14, 15, 16, 8], see also [17].”
- Quantum Entanglement in Neural Network States (2017, background): “tackling a variety of many-body problems ranging from the classification of topological phases [13, 14] to the construction of the Ads/CFT correspondence [15, 16].”