Just to be clear for a general reader. These are quasiparticles. They are effective mathematical descriptions of certain effects in the real world, but the physical particles responsible for the effects are fermions and bosons, not anyons.
It might have been a good joke initially, but it should not have persisted as a scientific name.
The termination "-on" in the Ancient Greek words "electron" and "proton" does not have any concrete meaning, it is just the thematic vowel "o" followed by the marker "n", of a singular neuter noun (originally "m", but in Ancient Greek all final "m" became "n").
Combining some undeclinable English word with an Ancient Greek case termination seems ugly and pointless for me (not that "fermion" and "boson" are any better from this point of view).
Even if we accept making words to rhyme as a technique for coining new words, "anyon" remains a bad choice, because it is easily confused with "anion" (introduced by Faraday almost two hundred years ago).
I assume that "anyon" is meant to have a different pronunciation, i.e. like "any-on", but nonetheless, in almost all other languages the vowels are pronounced different than in English and the default pronunciation for "anyon" and "anion" will likely be the same.
The reference to Ancient Greek is a matter of taste, I prefer new words to either have a meaning or to have no meaning, i.e. to be random. I find words with nonsense meaning irritating and more difficult to remember.
At least "fermion" is just a distorted form of Fermi, which does not suggest any specific meaning.
On the other hand "any on", has a meaning, but a nonsensical one, i.e. its suggests a reference to any one of the "ons", but there is no such thing as an "on", as that is just a grammatical case marker.
By the way, the "-on" in "anion" is not the same as the "-on" in proton. While the "-on" in proton comes from "-om", the "-on" in anion comes from "-ont", which corresponds to the English "-ing", the suffix of the active participle (anion = upwards-going).
For some weird reason, condensed matter physicists keep giving their quasiparticles the same names particle physicists give their particle particles, even though the mathematics are quite different. If you hear someone proclaiming the discovery of Majorana fermions, axions, or monopoles, it's essentially guaranteed to be a quasiparticle in a lump of metal or something. Sometimes even the articles themselves get confused about this.
Both are collective behaviors but most of the time you can think of protons as “balls made of quarks.” It’s not quite right but with semi classical treatment you get most of the effects. Anyons are not even approximately balls made of electrons. They break a lot of “classical particle” intuition the way protons don’t.
I wanted to highlight for a general reader that anyons are not particle in the sense of common intuition.
Protons, which the article brings as an example of collective phenomenona, roughly follow a lot of “particle intuition.”
Personally, I don’t mind if folks reify these things to make it easier to follow, fwiw.
That intuition is also most likely completely wrong.
Electrons in a material are effective particles, with a different mass, vide https://en.wikipedia.org/wiki/Effective_mass_(solid-state_ph....
Partice != fundamental particle.
Now, there's nothing wrong with exploring those ideas and they might eventually be fruitful, but in terms of looking "further down" (which is typically the lure of the excitement), quasiparticles are only looking back up. I am of the mind that you could make assemblages of particles -- that is to say, quasiparticles -- do all kinds of oddball things that their constituents cannot. That is fine and often useful, but it isn't the further down we were interested in.
Some elementary particles (quarks) don't really obey a lot of this intuition. Some none-elementary particles, for example protons/neutrons, do follow a lot of this intuition. Even some topological order quasiparticle in CMP follow this intuition -- magnetic skyrmions can be localized, can be imaged, have particle-like scattering.
Anyons don't follow this particle intuition.
In particular photons travelling through a medium are usually viewed as quasiparticles travelling slower than the speed of light, rather than a complex system of interactions. These particles have exactly the same kinds of behaviour as normal particles, similar to photons except with mass.
Taking this further you might conclude that a soundwave isn't physical either. And sound is actually an examples of quasiparticles (phonons) when you get down to the quantum level.
Then again most people would be of the opinion that light propagates slower through solids like glass, but the photons in that description are quasiparticles (which have mass, unlike the photons in isolation). And quasiparticles share many properties that you'd normally expect only physical particles to have so it gets complicated.