Entanglement Renormalization and Holography

By Brian Swingle. 2009

954 citations recorded by the source corpus.

We show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The generalization is based upon organizing information in a quantum state in terms of scale and defining a higher-dimensional geometry from this structure. While states with a finite correlation length typically give simple geometries, the state at a quantum critical point gives a discrete version of anti-de Sitter space. Some finite temperature quantum states include black hole-like objects. The gross features of equal time correlation functions are also reproduced.

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

View Paper: https://www.semanticscholar.org/paper/751b2df1fac5349fde1e6c9d0d808539c86ce0b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. D. Harlow
3. D. Stanford
4. T. Takayanagi
5. J. Maldacena
6. L. Susskind
7. V. Hubeny
8. S. Raju

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. D. Stanford
5. J. Maldacena
6. V. Hubeny
7. S. Raju
8. L. Susskind

In Statistical and Nonlinear Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. D. Stanford
5. S. Raju
6. Thomas Hartman
7. J. Maldacena
8. V. Hubeny

Citations in the corpus

• Multiboundary wormholes and holographic entanglement (2014, background): “From a different perspective, it has been been proposed that the general structure of the entanglement-based MERA ansatz for calculating ground state wavefunctions may provide a new understanding of the emergence of an additional dimension in the holographic description [12].”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “This approach seems more natural from the point of view of “ER=EPR” [84–88], but it seems like it cannot be consistent with linearity unless we consider only rather small code subspaces.”
• Circuit complexity in interacting QFTs and RG flows (2018, neutral): “ calculations have been generalized for free fermions in [17,19]. Interesting connections were found with holographic proposals in spite of the fact that these were free theories. It was suggested in [69] that tensor network approach maybe useful to derive qualitative features of holography, especia”
• Chaos and complexity by design (2016, background): “75 [78] B. Swingle, “Entanglement Renormalization and Holography,” Phys.”
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “[42] Brian Swingle.”
• Surface/State Correspondence as a Generalized Holography (2015, background): “In the paper [4], it has been argued that the mechanism of AdS/CFT can be understood as that of MERA if we consider discretizations (or lattice versions) of CFTs.”
• Chaos in quantum channels (2015, methodology): “k hole states that were perturbed by shock waves. Here, we provide a concrete model of such a network (i.e. we specify the tensors). This is in the spirit of previous work on the AdS ground state: in [38] it was suggested that the ground state of AdS can be represented by a hyperbolic tensor network”
• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “The implication (1) =⇒ (2) was noticed in examples such as the HaPPY and random tensor network codes already in [11, 13], with earlier hints going back to [69].”
• Integral geometry and holography (2015, background): “Swingle suggested [18, 19] that the MERA tensor network [20, 21] may be viewed as a discretization of the spatial slice of the holographically dual spacetime, because the latter – like MERA – also organizes the entanglement of the field theory state according to scale.”
• Hand-waving and interpretive dance: an introductory course on tensor networks (2016, methodology): “Imposing the graph metric on the MERA, we find a discretised anti-de Sitter (AdS) metric [17], whilst the edge theory is a ‘discretised’ CFT.”
• Generalized entropy and higher derivative gravity (2013, background): “Quantum entanglement appears to be a key ingredient for an understanding of holography [1, 2].”
• 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].”
• Entwinement and the emergence of spacetime (2014, neutral): “The relevance of boundary entanglement for such a reconstruction was first pointed out in [14, 15, 16, 8], see also [17].”