Figure 2
Examples of extra correlation holes in a 1D Pauli Anti-Crystal with N = 20 particles. By constructing Slater determinant of plane waves \({\psi }_{k}(x)=\frac{1}{\sqrt{L}}{e}^{i2\pi k\frac{x}{L}}\) with k = Δkn, where n = 1, …, N dips in g(x, y) are observed when x − y are multiples of \(\frac{L}{{\Delta }_{k}}\). Notice how the integrated volume of ρ(x, y)/N is exactly (N − 1) (if we exclude the delta function distribution at x = y) which means that the correlation hole accounts for precisely 1 particle. The correlation hole volume can thus not be made larger or smaller, but it can be reshaped, or even spit into several pieces.
