![\"What](\"https:\/\/www.newsbeep.com\/uk\/wp-content\/uploads\/2026\/02\/what-makes-an-anyon-1200x727.jpg\")
\u00a9 5W Infographics for Quanta Magazine<\/p>\nThe research, presented in two papers in Physical Review A, describes adjustable exchange statistics and a method to map them. It extends a concept once confined to two-dimensional materials into an even more constrained quantum setting.<\/p>\n
In the three-dimensional world, elementary particles are sorted into two categories defined by quantum spin and exchange behavior. Bosons, including photons, gluons, the Higgs boson, and the W and Z bosons, carry integer spin and can share the same quantum state. Fermions, protons, neutrons, electrons, and neutrinos, have half-integer spin and cannot occupy the same state, a rule that keeps matter structurally intact.<\/p>\n
That division has long appeared complete. Yet for decades, physicists have known of exceptions in lower dimensions. According to Popular Mechanics, researchers at the Okinawa Institute of Science and Technology (OIST) and the University of Oklahoma now report that the boson-fermion binary can also be broken in one dimension.<\/p>\n
A \u201cThird Kingdom\u201d Beyond Bosons and Fermions<\/p>\n
The idea of anyons emerged about 50 years ago as a theoretical possibility in two-dimensional systems. These quasiparticles behave as something between a boson and a fermion. American physicist Frank Wilczek coined the term \u201cany-on,\u201d suggesting they could take on \u201cany\u201d value between the two statistical limits.<\/p>\n
\u00a9 5W Infographics for Quanta Magazine<\/p>\n
Experimental confirmation came in 2020, when anyons were observed in one-atom-thick semiconductors. As reported by Popular Mechanics<\/a>, Wilczek described the achievement bluntly: \u201cWe had bosons and fermions, and now we\u2019ve got this third kingdom.\u201d He called it \u201cabsolutely a milestone,\u201d<\/a> marking the first direct evidence that particle statistics in two dimensions <\/a>can depart from the strict binary seen in three-dimensional space.<\/p>\n The Exchange Factor That Defines Particle Identity<\/p>\n The distinction between bosons and fermions<\/a> rests on what physicists call the exchange factor. In three dimensions, when two identical particles swap places, the square of this factor must equal 1. This mathematical requirement limits possibilities to two values: -1 for fermions and 1 for bosons.<\/p>\n Lower dimensions alter that rule. According to a press statement, Ra\u00fal Hidalgo-Sacoto, a Ph.D. student at OIST, explained that in two dimensions, \u201cto 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.\u201d Any value between -1 and 1 corresponds to an anyon.<\/p>\n Anyons exist in these reduced dimensions because particles have fewer options for moving around. The constraints of the space directly affect how their exchange statistics are defined.<\/p>\n Breaking the Binary in One Dimension<\/p>\n In the newly published studies, Thomas Busch and Ra\u00fal Hidalgo-Sacoto of OIST, together with Doerte Blume from the University of Oklahoma, describe a one-dimensional system where anyons can also arise. The researchers present both the theoretical properties of these particles <\/a>and a \u201crecipe\u201d for adjustable anyons<\/a>.<\/p>\n In one dimension, particles must pass through each other, since they cannot move around one another as they can in higher dimensions. This constraint changes the exchange factor, likely linking it to the strength of short-range interactions between particles. The team also demonstrates how the exchange statistics can be mapped<\/a>.<\/p>\n![\"Graphic](\"https:\/\/www.newsbeep.com\/uk\/wp-content\/uploads\/2026\/02\/graphic-illustration-of-the-papers-findings-a-knob-labelled-with-a-can-be-dialed-between-0-and-1-sho.jpeg\")
Graphic illustration of the papers\u2019 findings. A knob labelled with \u03b1 can be dialed between 0 and 1, showing how it affects the symmetry of two particles during an exchange operation, shown as two \u03a8s inside mathematical bra-ket notation \u2013 \u00a9 Jack Featherstone \/ EurekAlert<\/p>\n