The Fourier transform of the curvature function F ~ ~ ( R ) = ∫ ∫ d D k ( 2 π π ) D e i k ⋅ ⋅ R F ( k , M ) typically measures the overlap of certain quantum mechanical wave functions or more complicated objects, and therefore it is interpreted as a correlation function. For instance, if the curvature function is the noninteracting or many-body Berry connection or Berry curvature, the correlation function F ~ ~ ( R ) is a measure of the overlap of Wannier functions centered at two home cells that are distance R apart. Because of the Lorentzian shape of the curvature function mentioned above, the Fourier transform of the curvature function decays with the length scale ξ ξ . Hence, ξ ξ is interpreted as the correlation length, and its critical exponent is assigned to be ν ν like in Landau theory. Furthermore, the correlation length is related to the localization length of topological edge states, such as Majorana modes.