A pale green crystal was placed in a magnetic field and cooled below one kelvin — almost to absolute zero. Inside it hide chains of copper atoms that behave like tiny magnetic needles. Usually their orientation is chaotic, but the strong field and cold make the needles align in a unified impulse, like soldiers on a parade ground. At this transition moment, the three-dimensional crystal loses one dimension and starts behaving as if it were made of separate one-dimensional threads.
In such threads, unusual particles are born — not electrons or photons, but collective oscillations of magnetic order. Their set, or spectrum, turned out to be not random. It exactly matches the predictions of an integrable field theory associated with E8 symmetry — one of the most beautiful and complex mathematical structures. It's as if a melody suddenly emerged from the noise of a crowd, written according to notes that previously existed only on paper.
The energies of these particles were measured using neutron scattering. The masses of the excited states fell on the calculated curve with jewel-like precision. This means that a hidden symmetry briefly emerged in the material, one that no one had ever seen in three-dimensional systems. For an instant, the crystal became a perfect one-dimensional universe obeying laws derived for a completely different world.
When the field was removed, the green crystal became just a crystal again. But the spectrum remained in the data, like a photograph of a visitor from another dimension. Now physicists have a bridge between abstract mathematics and real materials. And who knows what other symmetries hide in other magnets, waiting for their moment.
E8 symmetry is so complex that its mathematical description would fill an entire book, yet here it appeared in a crystal the size of a grain of rice.
In Carl Sagan's novel "Contact," aliens hide a message in the number pi — perhaps E8 symmetry will also turn out to be a universal key.