This might be a too broad or superficial question, but unfortunately I cannot make it more concrete since I know little about QFT vacuum structure, and even less about Wen's study entanglement.
That said, there's an obvious resemblance between the two. Wen's study is mostly set up on a lattice system, with the Hilbert space being the product of local Hilbert spaces on the lattice sites. On the other hand, for example, in lattice Yang-Mills, the situation is very much the same. Since it seems Wen has studied quite a lot on many-body ground state entanglement, I wonder if any of his methods can shed light on, say, the vacuum structure of Yang-Mills theory? And QCD with fermionic matter? Or any other relativistic QFT model?