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Topological phase transitions track changes in topological properties of asystem and occur in real materials as well as quantum engineered systems, allof which differ greatly in terms of dimensionality, symmetries, interactions,and driving, and hence require a variety of techniques and concepts to describetheir topological properties. For instance, depending on the system, topologymay be accessed from single-particle Bloch wave functions, Green's functions,or many-body wave functions. We demonstrate that despite this diversity, alltopological phase transitions display a universal feature: namely, a divergenceof the curvature function that composes the topological invariant at thecritical point. This feature can be exploited via a renormalization-group-likemethodology to describe topological phase transitions. This approach serves toextend notions of correlation function, critical exponents, scaling laws anduniversality classes used in Landau theory to characterize topological phasetransitions in a unified manner.

Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems