Universal tripartite entanglement in 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 have nontrivial tripartite entanglement. We then establish that in 1D these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we show that either g is positive and h=0 or both are zero, depending on whether the ground state has long-range order. For a critical system, we develop a novel numerical algorithm to compute g and h from lattice models. 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. Finally, we discuss the implications of our results for holography.