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Comment by johncarlosbaez | Hacker News Reader

I've never seen a good clear explanation of "fractionalization" - the way that that systems can contain excitations that act like particles with charges that are a fraction of the electron charge. A typical non-explanation:

https://scitechdaily.com/quantum-revolution-redefining-physi...

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Couldn't an effective theory/mean-field theory have almost any emergent behavior depending on the underlying configuration space/system? Kind of like how one can build a domain-specific language out of an expressive enough underlying language it's implemented in

Maybe, but getting fractional charges out of a system with charges that are integer multiples of the electron charge is no mean feat, and I want to understand the math behind this in detail. Someone knows, but I haven't found any clear explanations.

I'm no physics expert but I do make programmable crystals for a living. One of my favorite applications of adiabatic quantum computers is the simulation of physical materials such as [1] wherein we see emergent phenomena like fractional magnetization. My contribution to this paper was to find the configuration of qubits equivalent to the material in question. What's really cool about experiments like this is that you can directly observe the spin configurations that give rise to the fractional states -- if you're sufficiently motivated, you could reproduce the experiment and paw through the data yourself (disclaimer: that may require you to pay my employer for QPU access). For the less motivated, see figure 3.

[1, lay coverage] https://csmd.ornl.gov/highlight/quantum-computing-enables-si...

[1, free PDF] https://arxiv.org/pdf/2003.01019

The way my inner child handwaves it away: you have the electron wavefunction spread out, say, it’s equally likely to be in one of 2 points in space. If you only look at one of these 2 points, you are likely to measure only half an electron.. until an adult (say, you) corrects me (using the Feynman Dirac hand/belt trick)

That explains having a 50% chance of seeing an electron somewhere, not seeing an entity of charge 1/2. It's like a weather report saying there's a 50% chance of rain doesn't mean you're going to see little raindrops cut in half.

If you look at the experiments, they don’t mention observing a single entity of fractional charge, it is always in terms of aggregate behavior under EM fields: conductance(1) inferred from shot noise (2), or density (3)

(1) https://arxiv.org/pdf/0912.4868

(2) https://n.ethz.ch/~marnikm/files/shotNoise.pdf

(3) https://www.researchgate.net/profile/Gerhard-Abstreiter/publ...

Personally, I find it curious that people talk about detecting single photons, but in these fractional charge experiments, nobody mentions detecting a single quasiparticle.

As for the math, nobody says it outright, or even in a single paragraph, but a fractional charge (“filling fraction”) of p/q does correspond to p “normal” charges distributed over q degenerate states (q=2 equivalent locations I used in the naive example)

https://xgwen.mit.edu/sites/default/files/documents/topWN.pd...

> Personally, I find it curious that people talk about detecting single photons, but in these fractional charge experiments, nobody mentions detecting a single quasiparticle.

You detect a single photon when it perturbs an apparatus like a photon multiplier; you detect a single quasiparticle when it perturbs a split stream of electrons.

The apparent difference is that photons can travel through free space and strike such an apparatus from afar; while quasiparticles definitionally cannot. However, I’ve read about experiments that measure a single anyon on a dot by wrapping electron interferometry around it, which is measuring the lone quasiparticle on that dot.

So I don’t follow your point.

Thank you for keeping me on my feet!

You probably mean the following (note the nuance and date of the first one):

https://arxiv.org/pdf/2403.12139.pdf

https://www.nature.com/articles/s41567-020-1019-1

I still think my point, originally about 1 electron split into 2 locations, or “ends” of string (but devolving to a complaint about casual ignorance of the central issue in publications) hasn’t been completely destroyed, because here you are measuring interference of 2 anyons, somewhat like measuring the interference of a photon “with itself” in a double split experiment.

The broader point could be that the effect of a single photon is “localized”, but here to see the effect, you have to move 1 anyon in a “complete path” around the other, recalling the Feynman/Dirac belt in my top level comment, a trick I said an adult should try to correct me with :)

There is only a difference if you observe the position.

When interactions happen only between particles that are all spread through that same space, both look the same.

do fractional electrons when perturbed radiate fractional photons?

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