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I am reading on fractons. In the literature, it is said that factons are fractionalized excitations.

My understanding about fractons is that it is energetically costly to move fractons, and in this sense, fractons are intrinsically immobile. I also know that there are two types of fractons where type I fractons can form composite quasiparticles, which are mobile, and type II fractons are fundamentally immobile as the energy cost for moving them is infinite.

However, I have not seen much discussion about how fractons are "fractionalized" excitations. I recall from my reading on quantum Hall effects that the name "fractionalized" excitation is associated with the fractional statistics (i.e. topological spin) of quasiparticles in the context of fractional quantum Hall effect. What does this "fractionalization" mean in the context of fractons? Are these two notations of "fractionalized" excitations related?

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    $\begingroup$ I think the name derives rather from the fractal structures formed by type II fractons. $\endgroup$
    – Norbert Schuch
    Commented Mar 23, 2021 at 22:37
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    $\begingroup$ @NorbertSchuch I thought so too! Turns out it is wrong: see d_b's answer below $\endgroup$
    – Ruben Verresen
    Commented Mar 24, 2021 at 3:17
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    $\begingroup$ @Ruben Interesting, but no reason to stop spreading the belief that it comes from their fractal nature, I think it makes for a much nicer story :) (Also, all anyons fractionalize quantum numbers, so it is indeed a somewhat oddly chosen name.) $\endgroup$
    – Norbert Schuch
    Commented Mar 24, 2021 at 10:31
  • $\begingroup$ @NorbertSchuch I think you are probably right that the authors had "fractal" in the back (or front) of their minds when coining "fracton," but I couldn't find published evidence of this. $\endgroup$
    – d_b
    Commented Mar 30, 2021 at 19:16
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    $\begingroup$ @d_b Hm, it could be both "fractal" or "fractional". We should ask them. $\endgroup$
    – Norbert Schuch
    Commented Mar 30, 2021 at 20:36

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The name "fracton" was coined by Vijay, Haah, and Fu (https://arxiv.org/abs/1505.02576) precisely because of the phenomenon you have described: individual fractons are immobile, but composites of multiple fractons may not be.

Composites of these fundamental excitations, however, are topological excitations that are free to move within sub-manifolds of the d-dimensional lattice. We term these fundamental excitations that behave as fractions of mobile particles, “fractons.”

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