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Title: Entanglement transitions from holographic random tensor networks

Abstract

Here, 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.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics
  2. Univ. of Texas, Austin, TX (United States). Dept. of Physics
  3. Harvard Univ., Cambridge, MA (United States). Dept. of Physics; Univ. of California, San Diego, CA (United States). Dept. of Physics
  4. Univ. of California, Santa Barbara, CA (United States). Dept. of physics
Publication Date:
Research Org.:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1569745
Grant/Contract Number:  
SC0019168
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 13; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Quantum entanglement; tensor networks

Citation Formats

Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, and Ludwig, Andreas W. W. Entanglement transitions from holographic random tensor networks. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.134203.
Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, & Ludwig, Andreas W. W. Entanglement transitions from holographic random tensor networks. United States. doi:10.1103/PhysRevB.100.134203.
Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, and Ludwig, Andreas W. W. Wed . "Entanglement transitions from holographic random tensor networks". United States. doi:10.1103/PhysRevB.100.134203.
@article{osti_1569745,
title = {Entanglement transitions from holographic random tensor networks},
author = {Vasseur, Romain and Potter, Andrew C. and You, Yi-Zhuang and Ludwig, Andreas W. W.},
abstractNote = {Here, 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.},
doi = {10.1103/PhysRevB.100.134203},
journal = {Physical Review B},
number = 13,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}

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