Symmetry is one of the most fundamental concepts in modern physics. In condensed matter and statistical physics, the classical theoretical framework for understanding phases and phase transitions is Landau’s theory of spontaneous symmetry breaking, which characterizes different phases through local order parameters. However, certain quantum phases—such as topological phases—cannot be described within this traditional framework.

To understand these phenomena, it is necessary to introduce a more general concept of symmetry, known as generalized symmetry, and to develop new theoretical frameworks.

Order parameters play a central role in detecting spontaneous symmetry breaking within Landau theory. Similarly, in topological quantum matter, one aims to construct topological order parameters based on generalized symmetries to characterize topological phases and their phase transitions, thereby exploring possible extensions of the traditional Landau paradigm.