Abstract
Abstract 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.
Highlights
Gauge topology is a fundamental aspect of modern field theory
In this paper we will pay our special attention to the Fourier entropy and the snapshot entropy defined by spatial distribution of ρ(x), which will be useful for our image-processing purpose
The Fourier power spectrum is a useful device for the image processing, and a more conventional alternative is the singular value decomposition (SVD) analysis which is suitable for coarse-graining the image
Summary
Gauge topology is a fundamental aspect of modern field theory. It would be an ideal setup for theoretical investigations if a system is simple but still nontrivial enough to accommodate nonvanishing topological winding. We point out that recent developments of condensed matter physics experiments has enabled us to emulate the CP N−1 model and its variants on the optical lattice [21] In this way, the CP N−1 is a relatively simple and well-established model, many interesting studies are ongoing to the present date. [33] for a recent review) It is still a challenging problem how to access topologically nontrivial sectors generally in field theories. We perform the Fourier power spectrum analysis of the topological charge density This power spectrum amounts to a momentum dependent generalization of the topological susceptibility, which has been discussed and partially measured in QCD in Refs.
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