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Entanglement transitions from holographic random tensor networks

Romain Vasseur, Andrew C. Potter, Yi-Zhuang You, and Andreas W. W. Ludwig
Phys. Rev. B 100, 134203 – Published 9 October 2019

Abstract

We introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

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  • Received 24 March 2019
  • Revised 14 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.134203

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Romain Vasseur1, Andrew C. Potter2, Yi-Zhuang You3,4, and Andreas W. W. Ludwig5

  • 1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 2Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
  • 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4Department of Physics, University of California, San Diego, California 92093, USA
  • 5Department of physics, University of California, Santa Barbara, California 93106, USA

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Issue

Vol. 100, Iss. 13 — 1 October 2019

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