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Particles in disorder behave like frozen glass, but not all at once.
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Ice cubes in a glass melt, and the water mixes on its own. Many quantum systems behave this way: particles exchange energy, and after a while, order disappears. But if you add a spoonful of honey to the glass, mixing slows down, and in intense cold, the water freezes into glass — without a crystal lattice, but also without flow.
Physicists built a two-dimensional lattice of superconducting qubits, tiny quantum switches, and introduced deliberate disorder. With weak disorder, the spins, i.e., the magnetic moments of the particles, moved freely, like molecules in warm water. But when disorder was increased, the system entered an intermediate state: some spins froze, as in glass, while others kept wiggling. This is evident from the fact that the probability of returning to the initial state decayed slowly, following a power law, rather than quickly as in a normal liquid.
In glass, atoms get stuck in random positions instead of arranging into a crystal. Here it's the same, but at the quantum level: some spins are frozen, others are not.
It turned out that in this regime, spin diffusion disappears: they stop spreading across the system. At the same time, an order parameter appears, which is typically associated with the glassy phase. This means that two-dimensional quantum systems can have a transition from an ergodic phase, where everything mixes, to a non-ergodic one, resembling glass.
Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting qubits, we study an interacting spin model at finite temperature in a disordered landscape, tracking dynamics both in real space and in Hilbert space. Over a broad disorder range, we observe an intermediate non-ergodic regime with glass-like characteristics: physical observables become broadly distributed and some, but not all, degrees of freedom are effectively frozen. The Hilbert-space return probability shows slow power-law decay, consistent with finite-temperature quantum glassiness. In the same regime, we detect the onset of a finite Edwards-Anderson order parameter and the disappearance of spin diffusion. By contrast, at lower disorder, spin transport persists with a nonzero diffusion coefficient. Our results show that there is a transition out of the ergodic phase in two-dimensional systems.
