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Though, what I was really looking for was a canonical/authorative CMT text which would say clearly that or when topological order requires strong interaction.
Most texts say this only in between the lines, with a sequence of implications like
$\text{strong interaction} \;\Rightarrow\; \text{long-range entanglement} \Rightarrow \text{topological order}$tacitly understood.
But I was hoping for a more explicit form of the statement that could easily be cited. Preferably a boxed statement of the kind they have in Quantum Information Meets Quantum Matter.
Found an honest explicit comment on the first arrow,
from Zaanen, Liu, Sun & Schalm 15, p. 527:
In a way it appears obvious that the strongly interacting bosonic quantum critical state is subject to long-range entanglement. Nonetheless, the status of this claim is conjectural.
It is at present impossible to arrive at more solid conclusions that are based on rigorous mathematical procedures. It does illustrate emphatically the central challenge in the pursuit of field-theoretical quantum information: there are as yet not general measures available to precisely enumerate the meaning of long- range entanglement in such seriously quantum field-theoretical systems.
Thanks. Right, I had left out the more speculative Section 11.
But string net models as such are really discussed in section 6. I have now added a link to string-net model there. The article which this points to currently remains what we call a “stub”. Please feel invited to edit and expand.
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