Electrons in a thin layer are like a flock of birds: each dodges its neighbors due to electric repulsion, yet together they generate waves — an electron plasma (a charged gas). Their collective behavior is described by a wave function — a mathematical script of all possible positions at once, including quantum superposition. Such calculations are usually cumbersome, but scientists trained a neural network to find patterns on its own. It processed the coordinates of up to 169 electrons and delivered a result more accurate than traditional computational methods.

Studying measurable characteristics, the researchers noticed an unexpected dip in the oscillation energy — a roton minimum. The same effect was described by Richard Feynman in superfluid helium, and it signals the imminent freezing of a liquid into a crystal. So, electrons, like birds ready to land in strict formation, send out a crystallization signal beforehand. Quantum entanglement binds them into a single organism.

This breakthrough turns artificial intelligence into a universal microscope for quantum matter. On the horizon: designing room-temperature superconductors and unraveling exotic states.