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Hyperbolic fracton model, subsystem symmetry, and holography

Han Yan (闫寒)
Phys. Rev. B 99, 155126 – Published 15 April 2019

Abstract

We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti–de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the holographic tensor networks, which illuminate the quantum-error-correcting properties of gravity in the anti–de Sitter space. In this work we discuss a classical toy model featuring subsystem symmetries and immobile fracton excitations. We show that such a model defined on the hyperbolic lattice satisfies some key properties of the holographic correspondence. The correct subregion duality and Ryu-Takayanagi formula for mutual information are established for a connected boundary region. A naively defined black hole's entropy scales as its horizon area. We also present discussions on corrections for more complicated boundary subregions, the possible generalizations of the model, and a comparison with the holographic tensor networks.

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  • Received 27 September 2018
  • Revised 20 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.155126

©2019 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Han Yan (闫寒)*

  • Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan

  • *han.yan@oist.jp

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Issue

Vol. 99, Iss. 15 — 15 April 2019

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