Linhao Li

The quantum world loves order, but reality often brings disorder. In this work, physicists study one-dimensional chains of spins — tiny magnetic arrows that can point up or down. Usually, topological phases (stable states protected by symmetry) are defined for pure states, where each arrow is precisely known.

In a mountain range, there are trails that can be contracted to a point if you walk through a flat valley. But there are also loop routes that cannot be shrunk without crossing a ridge.