Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

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 ha...

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Bibliographic Details
Published in:Physical review letters 2021-03, Vol.126 (12), p.120501-120501, Article 120501
Main Authors: Zou, Yijian, Siva, Karthik, Soejima, Tomohiro, Mong, Roger S K, Zaletel, Michael P
Format: Article
Language:English
Subjects:
Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Conformal field theory
Continuous phase transition
Energy theory
Entanglement
Gauge-gravity dualities
Long range order
Matrix product states
Numerical analysis
Quantum entanglement
Quantum spin chains
Tensor network methods
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.126.120501