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added these pointers on classification of topological phases of matter via tensor network states:
C. Wille, O. Buerschaper, Jens Eisert, Fermionic topological quantum states as tensor networks, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)
Andreas Bauer, Jens Eisert, Carolin Wille, Towards a mathematical formalism for classifying phases of matter (arXiv:1903.05413)
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In that introductory paragraph
… if external adiabatic deformations of the system that are gentle enough not to excite modes beyond energy >Δ above the ground state leave the properties of the system invariant if the deformations are small…
the final “if the deformations are small” is a repetition? The whole paragraph being a single sentence it’s hard to parse.
Thanks! That’s much clearer.
added pointer to this review:
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Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen:
Quantum Information Meets Quantum Matter – From Quantum Entanglement to Topological Phases of Many-Body Systems, Quantum Science and Technology (QST), Springer (2019) $[$arXiv:1508.02595, doi:10.1007/978-1-4939-9084-9$]$
Will add this also to several further related pages.
7:
I have renamed the entry from “topological state of matter” to “topological phase of matter”. The latter is the established terminology,
Good, we trust you that it is more widely used, you are now a prominent researcher in the subject.
and the former doesn’t really make sense.
It is in the same sense as in “solid state physics” and some prominent group do use the terminology, e.g. at Brown Univ. here or in these seminars in Koeln or in this Nature review from 2017. Never mind, the existing redirect is enough of course.
But I visited this page for another, more important, reason: are you interested (I see no pages on this topic but some people around me talk about it) in fracton phases of matter ? I was thinking to record few references on fractons but I do not see how it fits in $n$Labs big scheme of the wider subject of topological phases. Any advice, thought ?
Regarding terminology: I am not dogmatic about preferring “topological phase of matter” over “topological state of matter”, though I still feel the former makes better sense. But I have added mentioning of the alternative in the first line of the Idea-section (here) and I have added pointer to Wang & Zhang (2017).
Regarding fractons: I have seen some of the articles but haven’t really looked into the topic, so at this point I don’t know how it fits into a broader picture.
The broad description of fractons – as objects stuck at one position unless forming a suitable bound state – is quite reminiscent of that of fractional D-branes – which are stuck at an orbi-singularity unless they bind to (have a direct sum of D-brane charges equivalent to) a regular representation. This similarity may be profound or superficial, I don’t know; the actual constructions used in fracton theory (e.g. in arXiv:2001.01722) look rather different from such fractional D-branes.
I have seen some reference where some models with fractons are indeed obtained from some brane models, but those did not look general enough. “At one position” may be in the sense that some of the dimensions are constrained and other not suggesting foliation like spacial structure, and some people indeed use foliations to model this (“foliated quantum field theory”).
Not sure how compelling I find this foliated story, but admittedly I have only glanced over it.
But it may be worth highlighting that the story of fractional branes is bound to re-appear in topological phases of matter — as soon as the widely expected (and indeed plausible) conjecture is true that symmetry-protected crystalline topological phases are classified by (twisted) equivariant K-theory:
Namely, fractional D-branes are effectivley entirely characterized by their reflection in the equivariant K-theory around orbi-singularities. So exactly the same mathematical arguments will give a directly analogous physical effect at fixed points of the point group symmetry of crystals in topological phases.
I don’t recall that this has been considered and given a name in solid state physics before, but it seems inevitable that it’s there. And these CMT-analogs of fractional branes are guaranteed to obey at least the informal description of fractons…
Interesting, I will try to read more to fully appreciate this idea.
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added pointer to today’s:
this item seems to be only marginally about topological phases of matter:
A better place to record this would be at quantum anomaly and renormalization.
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