In the quantum world, there are rules that seem to be broken. One of them is the conservation law: if in classical physics symmetry guarantees the conservation of charge, then in the quantum description this guarantee can disappear. This phenomenon is called a quantum anomaly. It is not an error but a special property that manifests in unusual responses of the system.

One striking example is the parity anomaly of a two-dimensional Dirac fermion. Under normal conditions, an electric current in a two-dimensional system under a magnetic field flows strictly transverse, and its magnitude is an integer multiple. But at the point where parity symmetry is restored, the current becomes "half-integer"—exactly half of the standard quantum. For a long time, this effect was observed only on the surface of three-dimensional materials, while in a purely two-dimensional system it remained elusive.

Now researchers from the University of Science and Technology of China used ultracold dysprosium atoms. They created a synthetic two-dimensional space: one dimension is real, and the second is "glued" from the spin states of the atoms. This allowed them to engineer topological bands with different Chern numbers. At the transition point between bands with numbers 0 and 1, the energy gap closes at a single point — the Dirac point. There, the anomalous response appeared: the drift of atoms showed half quantization despite strong excitations.

This result is not just a beautiful demonstration. It shows that synthetic quantum systems can serve as a clean playground for studying anomalies and their connection to topology. In the future, such platforms will help test subtle predictions of quantum field theory and possibly discover new states of matter.