Image-processing the topological charge density in the $\mathbb{C}P^{N-1}$ model

We study the topological charge density distribution using the 2D $\mathbb{C}P^{N-1}$ model. We numerically compute not only the topological susceptibility, which is a spatially global quantity, to probe the topological properties of the whole system, but also the topological charge correlator with finite momentum. We perform a Fourier power spectrum analysis for the topological charge density for various values of the inverse temperature $\beta$. We propose to utilize the Fourier entropy as a convenient measure to characterize spatial distribution patterns and demonstrate that the Fourier entropy exhibits nontrivial temperature dependence. We also consider the snapshot entropy defined with the singular value decomposition, which also turns out to behave nonmonotonically with the temperature. We give a possible interpretation suggested from the strong-coupling analysis.