Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence

Bao, Ning; Cao, ChunJun; Carroll, Sean M.; Chatwin-Davies, Aidan; Hunter-Jones, Nicholas; Pollack, Jason; Remmen, Grant N.

doi:10.1103/PhysRevD.91.125036

Title: Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence

Abstract

The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an anti–de Sitter (AdS) spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. In this report, we explore this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Similarly, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.

Authors:

Bao, Ning ^[1]; Cao, ChunJun ^[2]; Carroll, Sean M. ^[2]; Chatwin-Davies, Aidan ^[2]; Hunter-Jones, Nicholas ^[2]; Pollack, Jason ^[2]; Remmen, Grant N. ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Publication Date:: Mon Jun 29 00:00:00 EDT 2015

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Gordon and Betty Moore Foundation; National Science Foundation (NSF)

OSTI Identifier:: 1599371

Alternate Identifier(s):: OSTI ID: 1198616

Grant/Contract Number:: SC0011632; DGE-1144469

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. D, Particles, Fields, Gravitation and Cosmology

Additional Journal Information:: Journal Volume: 91; Journal Issue: 12; Journal ID: ISSN 1550-7998

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Bao, Ning, Cao, ChunJun, Carroll, Sean M., Chatwin-Davies, Aidan, Hunter-Jones, Nicholas, Pollack, Jason, and Remmen, Grant N. Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevD.91.125036.

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                    Bao, Ning, Cao, ChunJun, Carroll, Sean M., Chatwin-Davies, Aidan, Hunter-Jones, Nicholas, Pollack, Jason, & Remmen, Grant N. Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence.  United States.  https://doi.org/10.1103/PhysRevD.91.125036

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                    Bao, Ning, Cao, ChunJun, Carroll, Sean M., Chatwin-Davies, Aidan, Hunter-Jones, Nicholas, Pollack, Jason, and Remmen, Grant N. Mon .  
"Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence".  United States.  https://doi.org/10.1103/PhysRevD.91.125036.  https://www.osti.gov/servlets/purl/1599371.

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@article{osti_1599371,

  title        = {Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence},

  author       = {Bao, Ning and Cao, ChunJun and Carroll, Sean M. and Chatwin-Davies, Aidan and Hunter-Jones, Nicholas and Pollack, Jason and Remmen, Grant N.},

  abstractNote = {The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an anti–de Sitter (AdS) spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. In this report, we explore this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Similarly, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.},

  doi          = {10.1103/PhysRevD.91.125036},

  journal      = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},

  number       = 12,

  volume       = 91,

  place        = {United States},

  year         = {Mon Jun 29 00:00:00 EDT 2015},

  month        = {Mon Jun 29 00:00:00 EDT 2015}

}

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Title: Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence

Abstract

Citation Formats

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A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal, October 2014

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Proof of a quantum Bousso bound journal, August 2014

Time evolution of entanglement entropy from black hole interiors journal, May 2013

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Entropy on a null surface for interacting quantum field theories and the Bousso bound
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Nonlocal scaling operators with entanglement renormalization
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Algorithms for entanglement renormalization
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Black holes and the second law
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Class of Quantum Many-Body States That Can Be Efficiently Simulated
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Geometric and renormalized entropy in conformal field theory
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The Large-N Limit of Superconformal Field Theories and Supergravity
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Tensor Network States and Geometry
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Entanglement Renormalization for Quantum Fields in Real Space
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Entanglement, tensor networks and black hole horizons
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Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
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Classical simulation of quantum many-body systems with a tree tensor network
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Charged rotating black hole in three spacetime dimensions
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Bulk locality and quantum error correction in AdS/CFT
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