Holographic geometry of entanglement renormalization in quantum field theories

By M. Nozaki, S. Ryu, T. Takayanagi. 2012

247 citations recorded by the source corpus.

A bstractWe study a conjectured connection between AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction. The metric is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6a20997fe0458672073da1b48294fa2ee76ace28

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. Shira Chapman
3. H. Marrochio
4. T. Takayanagi
5. Masamichi Miyaji
6. M. Nozaki
7. Ro Jefferson
8. J. Sully

In Nuclear and High Energy Physics

1. R. Myers
2. Shira Chapman
3. H. Marrochio
4. T. Takayanagi
5. M. Nozaki
6. D. Harlow
7. Ro Jefferson
8. J. Sully

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. M. Nozaki
4. Shira Chapman
5. H. Marrochio
6. Ro Jefferson
7. J. Sully
8. B. Czech

Citations in the corpus

• Surface/State Correspondence as a Generalized Holography (2015, methodology): “Our proposal in this paper is highly motivated by this and the continuum version (called cMERA [14]) of this conjecture, studied in [15, 16, 17].”
• Circuit complexity in fermionic field theory (2018, methodology): “We will begin with Dirac fermions in 1þ 1 dimensions, which is a standard context where the cMERA tensor network is discussed [6,7], with an eye towards our discussions in the next section.”
• Holographic local quenches and entanglement density (2013, background): “In [41], this correspondence has been studied in the continuum limit (i.”
• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “Nevertheless, explicit formulations of cMERA are so far only available for free field theories [5] (see [7, 8, 20, 21] for various studies) which is the opposite regime from the strongly interacting CFTs which possess gravity duals, the so-called holographic CFTs.”
• Integral geometry and holography (2015, background): “3 The The analogy between holography and tensor networks was further advanced in [22–26]; see also [27] for a critique of associating MERA directly with the spatial slice of AdS3.”
• Complexity and entanglement for thermofield double states (2018, background): “[120, 121] and it was reported there, in the language of ref.”