Representation of extended operators and topological defects in the 3D X-cube model. Membrane operators (gray plaquettes) create fracton defects (cyan cubes). String operators (cyan lines) create lineon defects (red ellipsoids).

From the article:

Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
Hao Song (宋昊), Janik Schönmeier-Kromer, Ke Liu (刘科 子竞), Oscar Viyuela, Lode Pollet, and M. A. Martin-Delgado
Phys. Rev. Lett. 129, 230502 (2022)

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