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Title: Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Abstract

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

Authors:
 [1]; ORCiD logo [2];  [2];  [3];  [4]
+ Show Author Affiliations
  1. Sandbox@Alphabet, Mountain View, CA (United States); Univ. of Waterloo, ON (Canada); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. Univ. of California, Berkeley, CA (United States)
  3. Univ. of Pittsburgh, PA (United States)
  4. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1822401
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 126; Journal Issue: 12; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal field theory; Continuous phase transition; Gauge-gravity dualities; Quantum entanglement; Matrix product states; Quantum spin chains; Tensor network methods

Citation Formats

Zou, Yijian, Siva, Karthik, Soejima, Tomohiro, Mong, Roger S. K., and Zaletel, Michael P. Universal Tripartite Entanglement in One-Dimensional Many-Body Systems. United States: N. p., 2021. Web. doi:10.1103/physrevlett.126.120501.
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Zou, Yijian, Siva, Karthik, Soejima, Tomohiro, Mong, Roger S. K., & Zaletel, Michael P. Universal Tripartite Entanglement in One-Dimensional Many-Body Systems. United States. https://doi.org/10.1103/physrevlett.126.120501
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Zou, Yijian, Siva, Karthik, Soejima, Tomohiro, Mong, Roger S. K., and Zaletel, Michael P. Mon . "Universal Tripartite Entanglement in One-Dimensional Many-Body Systems". United States. https://doi.org/10.1103/physrevlett.126.120501. https://www.osti.gov/servlets/purl/1822401.
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@article{osti_1822401,
title = {Universal Tripartite Entanglement in One-Dimensional Many-Body Systems},
author = {Zou, Yijian and Siva, Karthik and Soejima, Tomohiro and Mong, Roger S. K. and Zaletel, Michael P.},
abstractNote = {Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.},
doi = {10.1103/physrevlett.126.120501},
journal = {Physical Review Letters},
number = 12,
volume = 126,
place = {United States},
year = {Mon Mar 22 00:00:00 EDT 2021},
month = {Mon Mar 22 00:00:00 EDT 2021}
}
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Publisher's Version of Record
https://doi.org/10.1103/physrevlett.126.120501
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Works referenced in this record:

Matrix product state representations
journal, July 2007

  • Perez-Garcia, D.; Verstraete, F.; Wolf, M. M.
  • Quantum Information and Computation, Vol. 7, Issue 5&6
  • DOI: 10.26421/QIC7.5-6-1

Spectral Gap and Exponential Decay of Correlations
journal, April 2006

Robustness of Quantum Markov Chains
journal, October 2007

  • Ibinson, Ben; Linden, Noah; Winter, Andreas
  • Communications in Mathematical Physics, Vol. 277, Issue 2
  • DOI: 10.1007/s00220-007-0362-8

The entanglement of purification
journal, September 2002

  • Terhal, Barbara M.; Horodecki, Michał; Leung, Debbie W.
  • Journal of Mathematical Physics, Vol. 43, Issue 9
  • DOI: 10.1063/1.1498001

Negativity as the entanglement measure to probe the Kondo regime in the spin-chain Kondo model
journal, February 2010

Renormalization-Group Transformations on Quantum States
journal, April 2005

Critical and noncritical long-range entanglement in Klein-Gordon fields
journal, July 2009

Entanglement of Purification in Many Body Systems and Symmetry Breaking
journal, May 2019

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Matrix product states represent ground states faithfully
journal, March 2006

Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions
journal, January 2017

Entanglement of purification: from spin chains to holography
journal, January 2018

  • Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G.
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)098

Entanglement wedge cross sections require tripartite entanglement
journal, April 2020

Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
journal, April 2004

  • Hayden, Patrick; Jozsa, Richard; Petz, D�nes
  • Communications in Mathematical Physics, Vol. 246, Issue 2
  • DOI: 10.1007/s00220-004-1049-z

Conformal Fields and Operator Product Expansion in Critical Quantum Spin Chains
journal, January 2020

Entanglement of purification through holographic duality
journal, March 2018

Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
journal, September 2019

Entanglement properties of the harmonic chain
journal, October 2002

Emergence of conformal symmetry in quantum spin chains: Antiperiodic boundary conditions and supersymmetry
journal, January 2020

Three qubits can be entangled in two inequivalent ways
journal, November 2000

Derivation of Holographic Negativity in AdS 3 / CFT 2
journal, September 2019

Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model
journal, May 2018

Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
journal, May 2019

Conformal Data and Renormalization Group Flow in Critical Quantum Spin Chains Using Periodic Uniform Matrix Product States
journal, December 2018

An area law and sub-exponential algorithm for 1D systems
preprint, January 2013

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