Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to wedge cross-section, we introduce two related non-negative measures tripartite $g$ $h$. We prove structure theorems which show that states with nonzero or $h$ have nontrivial entanglement. then establish 1D these are universal quantities depend only on emergent low-energy theory. For a gapped system, argue either $g\neq 0$ $h=0$ $g=h=0$, depending whether ground state has long-range order. critical develop numerical algorithm for computing from lattice model. compute various CFTs depends central charge whereas whole operator content.