Universal tripartite entanglement in one-dimensional many-body systems

Nov 23, 2020
6 pages
Published in:
  • Phys.Rev.Lett. 126 (2021) 12, 120501
  • Published: Mar 23, 2021
e-Print:

Citations per year

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Abstract: (APS)
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.
Note:
  • 5+16 pages, 4+5 figures
  • General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
  • model: lattice
  • field theory: conformal
  • dimension: 1
  • entanglement
  • many-body problem
  • central charge
  • ground state
  • holography
  • long-range
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