Symmetry found hidden in supercold atoms

Complex E8 patterns detected in physical system

A beautiful math emerges from the acrobatic flips of supercold atoms in a magnetic field, researchers report in the Jan. 8 Science.

Scientists detected an elusive, complex symmetry known as the E8 Lie group in resonating particles, a symmetry long analyzed on paper but never seen in a physical system. The work suggests that this numerical grace may be hidden in other physical systems and may provide a mathematical link between quantum processes in condensed matter and the physics of the cosmos.

“Finding a mathematically exotic symmetry in a regular material we can find on Earth — well, it is mathematically beautiful and very interesting,” comments Robert Konik of Brookhaven National Laboratory in Upton, N.Y. Symmetries helped theoretical physicists to predict the existence of certain particles before they were detected and to explain phenomena such as superconductivity. E8 in particular may help describe the unseen dimensions in string theory. But the emergent E8 symmetry in this system may be nothing more than a mathematical curiosity, researchers say.

The team of scientists from England and Berlin began with chains of the magnetic material cobalt niobate, a material whose electrons have a preferred direction of spin — either up or down. The researchers chilled the cobalt niobate to a cool 40 millikelvins (-273.1Ë Celsius) and then applied a magnetic field to the material. Without this external magnetic field, the spins of the electrons would all align in the same direction, like in an ordinary magnet. But an external magnetic field applied from the right direction introduces a tension, and at some point the electrons prefer to align with that magnetic field instead of with their neighbors. The electron spins are associated with particle-like states, known as quasiparticles, in the system.

That’s when the magic happens. The system approaches what’s known as the quantum critical point, and blocks of quasiparticles begin changing their orientation, which is detectable with a neutron beam, says study coauthor Alan Tennant of the Helmholtz Association of German Research Centers in Berlin.

Bound by the externally applied magnetic field and the slight magnetic field that exists between chains, the quasiparticles start resonating at mathematically intriguing frequencies. Two of the frequencies occur in the ratio of the golden mean, the influential and aesthetically pleasing ratio of 1.618 often used in art and architecture, says Tennant. The ratios of five frequencies correspond to the complex E8 Lie group symmetry, which represents a 57-dimensional solid. Defining a location on this kind of shape requires 57 coordinates, making it much more elaborate than the three coordinates needed to define a point in ordinary space.

“It is quite remarkable to see a material in the lab behaving with such perfection,” says Tennant. Perhaps this veiled symmetry will also emerge in other physical systems and shed light on bigger questions, he says.

Others aren’t so sure. “To a certain degree, the story of modern physics is a story of symmetry,” says Konik. “But I wouldn’t say this is going to tell us more about the fundamental nature of the universe.”

Theorist Bogdan Dobrescu of the Fermi National Accelerator Laboratory in Batavia, Ill., also expressed caution. Mathematics and theoretical physics “often share the same language,” he says. “But I think that is where the story stops.”

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