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Universal Tripartite Entanglement in One-Dimensional Many-Body Systems
Yijian Zou1,2,3, Karthik Siva4, Tomohiro Soejima4
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
Physical Review Letters
|April 9, 2021
Summary
We introduce new measures of tripartite entanglement, g and h, inspired by holographic conjectures. These measures reveal universal properties of quantum entanglement in one-dimensional systems and critical theories.
Area of Science:
- Quantum Information Theory
- High Energy Physics
- Condensed Matter Physics
Background:
- Holographic conjectures relate entanglement measures to the entanglement wedge cross section.
- Understanding tripartite entanglement is crucial for quantum information and quantum gravity.
Purpose of the Study:
- Introduce novel non-negative measures of tripartite entanglement, denoted g and h.
- Investigate the properties and universality of these entanglement measures.
- Connect tripartite entanglement to emergent low-energy theories and critical phenomena.
Main Methods:
- Develop structure theorems to prove non-trivial tripartite entanglement for nonzero g or h.
- Establish universality in one-dimensional systems, dependent only on the low-energy theory.
- Create a numerical algorithm for computing g and h in lattice models of critical systems.
Main Results:
- Demonstrate that nonzero g or h implies nontrivial tripartite entanglement.
- Show that in 1D, g and h are universal, depending solely on the emergent low-energy theory.
- For gapped systems, either g≠0 and h=0 or g=h=0, linked to long-range order.
- For critical systems (CFTs), h depends only on the central charge, while g depends on operator content.
Conclusions:
- The introduced measures g and h provide new insights into quantum entanglement structure.
- Tripartite entanglement measures exhibit universality in 1D and critical systems.
- The behavior of g and h distinguishes between gapped phases with and without long-range order and characterizes CFTs.
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