Physicists rarely question one of the field’s most fundamental rules: every particle in the Universe is either a boson or a fermion. Those two categories cover everything – forces, matter, atoms, and light. Physicists have run experiments for nearly a century without finding an exception in ordinary three-dimensional space.
In two-dimensional materials, the rule begin to break down. A strange class of particles can exist there that falls between the two categories.
One dimension was assumed to be even more restrictive. Two new papers suggest that assumption may be wrong – and what they find in one dimension is stranger than anyone expected.
Two camps of particles
Walk into a physics class, and you’ll learn that nature serves up two kinds of elementary particles.
Bosons carry forces – photons, for example. Fermions make up matter, including electrons, protons, and neutrons.
The dividing line shows up when two identical particles trade places. When two bosons swap places, nothing changes. Fermions flip the whole system’s sign.
Physicists have only observed those two outcomes in three-dimensional space.
Locked at two
The reason the menu is so short comes from a quantum principle called indistinguishability.
Physicists cannot mark or color-code two identical electrons in any way. Swap them, and the new arrangement is physically identical to the old one.
That restriction forces the outcome into one of two possibilities. Either the swap leaves the system completely unchanged, or it flips it.
Those are the only options the physics allows. Bosons do the first. Fermions do the second.
A third option
In three dimensions, the split holds neatly. Drop down to two, and theorists have predicted something stranger for half a century: particles that don’t fit either category – ones that land somewhere between unchanged and flipped, in a range no ordinary particle ever reaches.
They call them anyons – any-ons, neither one nor the other. Predicted since the 1970s and first observed in 2020, they’re real – but only at the edge of two-dimensional materials.
That sighting only sharpened the question for Thomas Busch, who leads the Quantum Systems Unit at the Okinawa Institute of Science and Technology (OIST).
“Every particle in our universe seems to fit strictly into two categories: bosonic or fermionic. Why are there no others?” said Busch.
When space gets thin
Dimension changes the rules because of how particle paths weave through space and time. Three-dimensional space gives particles room to curve around each other when they swap – paths braid briefly, then untangle cleanly. The swap leaves no trace.
In two dimensions, that escape hatch closes. The paths become knotted in ways physicists cannot undo, and the outcome no longer has to fall into one of the two familiar categories.
A 2020 paper caught the effect in ultracold semiconductors under extreme magnetic fields. Raúl Hidalgo-Sacoto, a Ph.D. student in Busch’s group at OIST and lead author on both new studies, lays out the topology in plain terms.
“In lower dimensions, this exchange is no longer topologically equivalent to doing nothing. To satisfy the law of indistinguishability, we need exchange factors over a continuous range to account for the exchange, dependent on the exact twists and turns of the paths,” said Hidalgo-Sacoto.
Squeezed to a line
Push down one more dimension, and something new happens. In one dimension, particles can no longer take the long way around each other. They have to pass through. That single change rewrites the swap entirely.
Until this study, no one had worked out whether anyons could survive in one dimension at all – let alone what their behavior would look like.
The two OIST papers, co-authored with Doerte Blume at the University of Oklahoma, show that they can. They also reveal a property no one expected.
Turning the dial
The exchange factor in 1D isn’t locked at a single value. It can be dialed – tied directly to how strongly the particles interact at close range.
That kind of control is something physicists have wanted for decades.
Crank it one way, and the particles behave more like bosons. Turn it the other, and they look more like fermions. The particles no longer have a fixed identity. Instead, their behavior acts more like a dial.
What changes now
Ultracold atoms, chilled with lasers within a hair of absolute zero, are precisely the platform where one-dimensional physics gets done every day.
A recent experiment in Austria has caught anyonic behavior in a similar 1D ultracold gas, lending early support to the OIST picture.
“The experimental setups necessary for making these observations already exist,” said Busch. Groups in Japan, Europe, and the United States are positioned to run them.
The boson-fermion binary stops being a binary on the line. Not two options. A spectrum. Physicists gain a value they can tune continuously – one that opens a fresh corner of fundamental physics and could feed new kinds of quantum simulators.
The study is published in Physical Review A.
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