Wavefunction’s unconventional statistics manifested

Wavefunction’s unconventional statistics manifested. In three dimensions, exchanging identical particles has a simple effect on a wavefunction: no change for bosons, multiplication by −1 for fermions. In two dimensions, things are more complicated. Consider the two ways to switch identical particles “A” and “B” shown in the figure. Because the clockwise and counterclockwise switches can’t be continuously deformed into each other, 2D exchange doesn’t just swap coordinates; it also involves a topological component. When many particles are involved, the topological issues are correspondingly more complex, and exchange operations might not commute. In that case the particles are said to have non-abelian (that is, noncommuting) anyon statistics. Non-abelian anyons are more than a mathematical curiosity: Condensed-matter physicists have plausibly argued that the quasiparticles that participate in the so-called ν = 5⁄2 fractional quantum Hall state are objects of that type (see the article by Sankar Das Sarma, Michael Freedman, and Chetan Nayak in PHYSICS TODAY, July 2006, page 32 ). Now, Nayak (Microsoft Station Q and the University of California, Santa Barbara) and colleagues have, in the first calculation of its kind, explicitly demonstrated the compatibility of a specific popular candidate ν = 5⁄2 wavefunction with non-abelian anyon statistics. The key step, says MIT’s Frank Wilczek, was to map the wavefunction to a rather different physical system amenable to attack with a well-established battery of mathematical tools. Does the wavefunction studied by the Nayak team actually describe the ν = 5⁄2 state? That ball is in the experimentalists’ court. (P. Bonderson et al., Phys. Rev. B 83, 075303, 2011.)