# Can Wen's study on many-body entanglement shed light on QFT vacuum structures?

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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?
asked Jan 24, 2015
edited Jan 24, 2015
A large portion of Wen's work (and many, many others) focuses on the entanglement structure in gapped quantum phases, e.g. the ground state of discrete gauge theories. Looking at entanglement entropy and entanglement spectrum is extremely useful in identifying the universal "topological order" in the ground state. This is well-established now and has been applied in condensed matter research (e.g. numerical simulations of many-body systems). For Yang-Mills theory, e.g. pure SU(3) gauge theory, I believe it has been shown in lattice QCD simulations that the ground state is in the confined phase, which probably means that it is a "trivial" state containing no long-range entanglement. It may still have interesting structures in the entanglement, particularly if matters are included.
@Meng, thanks. I left matter sector out since I wasn't quite sure if Wen's work includes Grassmannian functionals, as are used in lattice QCD. Now I'll edit the question to include the matter sector.
@JiaYiyang I think these general results about entanglement structure and topological order hold true in fermionic systems.

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