Reflected entropy in random tensor networks II: a topological index from the canonical purification

Understand

In arXiv:2112.09122, we analyzed the reflected entropy ($S_R$) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section (EW) in holographic theories, $S_R=2 \frac{EW}{4G}$.

• In this paper, we discover further details of this duality by analyzing a simple network consisting of a chain of two random tensors.
• This setup models a multiboundary wormhole.
• We show that the reflected entanglement spectrum is controlled by representation theory of the Temperley-Lieb (TL) algebra.