Image-processing the topological charge density in the CP(N-1) model

TL;DR

This paper investigates the spatial distribution of topological charge density in the 2D CP(N-1) model using numerical methods, Fourier analysis, and entropy measures to understand temperature-dependent topological features.

Contribution

It introduces Fourier and snapshot entropy measures to analyze topological charge distributions and explores their nontrivial temperature dependence in the CP(N-1) model.

Findings

Fourier entropy varies nonmonotonically with temperature.

Snapshot entropy also shows nonmonotonic behavior.

Provides interpretation from strong-coupling analysis.

Abstract

We study the topological charge density distribution using the two-dimensional $CP^{N-1}$ model. We numerically compute not only the topological susceptibility, which is a spatially global quantity to probe topological properties of the whole system, but also the topological charge correlator with finite momentum. We perform 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.