Universal tripartite entanglement in one-dimensional many-body systems

TL;DR

This paper introduces universal measures of tripartite entanglement in 1D many-body systems, linking them to low-energy theories and holographic conjectures, with computational methods and results for various conformal field theories.

Contribution

It defines new tripartite entanglement measures $g$ and $h$, proves their structure, and demonstrates their universality in 1D systems, connecting to holography and low-energy theories.

Findings

$h$ depends only on the central charge of the CFT.

$g$ depends on the entire operator content.

Tripartite entanglement measures are universal in 1D systems.

Abstract

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 argue that either $g\neq 0$ 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.