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added pointer to today’s
I have taken the liberty of adding sizeable a paragraph to above of what the previous author had in the Idea-section (here).
Namely, when I entered this subject a while ago, I found the literature (and our entry here) somewhat mysterious as to what the intended definition of “topological order” actually is. In retrospect I can see how the thinking evolved, but I have tried now to add that kind of broad-stroke explanation (and only broad-stroke explanations seem to exist, so far) which I believe I might have profited from reading when I happened upon the subject first.
(And I am not claiming that there is not much room left for further clarification.)
To this point, I am taking the liberty of removing the following bit from the list of references:
Discussion in terms of extended TQFT, the cobordism theorem and stable homotopy theory is in
{#FreedMoore12} Daniel Freed, Gregory Moore, Twisted equivariant matter, arxiv/1208.5055 (uses equivariant K-theory to classify free fermion gapped phases with symmetry)
{#Freed14} Daniel Freed, Short-range entanglement and invertible field theories (arXiv:1406.7278)
Namely, the first of these does not consider topological order at all, and the second explicitly considers the case where it’s absent (the “invertibility” in the title refers to the ground state being 1-dimensional).
(I don’t mean to hide these references, of course, indeed they are prominently listed in entries where they belong, but I think it’s positively misleading to cite them here under “topological order”)
Okay, so I should just explain this point in the entry then: Have added a small paragraph (here), together with a pointer to a new entry short-range entanglement.
added (here) a bunch of the early articles using the terminology “topological order” – all by Wen, the earliest seems to be
Then I used this to reference the text in the Idea-section (here) a bit more.
added pointer to:
(which is really an interview with Xiao-Gang Wen)
have worked further on the Idea-section:
re-worked the paragraph by the previous author into what is now the first paragraphs here
gave the characterization via entanglement entropy its own Idea-subsection (here), now showing the sequence of schematic implications which I just mentioned in another thread (here)
I see, good point, thanks.
I had been wondering about calling this page differently. One might like it to end on “… of matter” to rhyme on “topological phases of matter” with its usual abbreviation to “topological phases”, when the context us clear. Unfortunately, established usage of the terminology in the CMT literature doesn’t seem to give much freedom here. But I am open for suggestions.
added pointer to:
this reference item does not seem to be about topological order:
added pointer to this recent article:
added pointer to today’s
added pointer to:
and this one:
added pointer to:
Periodic boundary conditions in position space are quite unrealistic in (condensed matter physics-)experiment, and yet much discussion of anyonic topological order has been made under this assumption — because the desired ground state degeneracy depends on it. A curious state of affairs.
I have started to collect some references in the Sandbox, will maybe make this an !include
-entry tomorrow.
Have now !include
-ed a list anyonic topological order on tori – references (see the logs for the !include
-entry there)
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