‘Milestone’ Evidence for Anyons, a Third Kingdom of Particles

Anyons don’t fit into either of the two known particle kingdoms. To find them, physicists had to erase the third dimension.

Dana Najjar | NAUTILUS-Abstractions

The existence of anyons was inferred from quantum topology — the novel properties of shapes made by quantum systems. Credit: David S. Hall, Amherst College, using code developed by Niles Johnson

Every last particle in the universe—from a cosmic ray to a quark—is either a fermion or a boson. These categories divide the building blocks of nature into two distinct kingdoms. Now researchers have discovered the first examples of a third particle kingdom.

Anyons, as they’re known, don’t behave like either fermions or bosons; instead, their behavior is somewhere in the middle. In an April 2020 paper published in Science, physicists have found the first experimental evidence that these particles don’t fit into either kingdom. “We had bosons and fermions, and now we’ve got this third kingdom,” said Frank Wilczek, a Nobel prize–winning physicist at the Massachusetts Institute of Technology. “It’s absolutely a milestone.”

What Is an Anyon?

To understand the quantum kingdoms, think of a drawing of loops. Imagine two indistinguishable particles, like electrons. Take one, then loop it around the other so that it ends up back where it started. Nothing seems to have changed. And indeed, in the mathematical language of quantum mechanics, the two wave functions describing the initial and final states must be either equal or off by a factor of −1. (In quantum mechanics, you calculate the probability of what you observe by squaring this wave function, so this factor of −1 washes out.)

If the wave functions are identical, your quantum particles are bosons. If they’re off by a factor of −1, you have fermions. And though the derivation may seem like a purely mathematical exercise, it has profound physical consequences.

Fermions are the antisocial members of the particle world. They never occupy the same quantum state. Because of this, electrons, which are fermions, get forced into the varied atomic shells around an atom. From this simple phenomenon arises most of the space in an atom, the astonishing variety of the periodic table, and all of chemistry.

Bosons, on the other hand, are gregarious particles, happy to bunch together and share the same quantum state. Thus photons, which are bosons, can pass through each other, allowing light rays to travel unimpeded rather than scattering about.

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