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Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Journal Article · · Physical Review Letters
 [1];  [2];  [2];  [3];  [4]
  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)
+ Show Author Affiliations
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.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1822401
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 12 Vol. 126; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Conformal field theory
Continuous phase transition
Gauge-gravity dualities
Matrix product states
Quantum entanglement
Quantum spin chains
Tensor network methods