Fig. 5: Properties of the ground-state of the spin 1/2 XXZ Hamiltonian on the ‘maximally irregular graph’ where each pair of vertices, other than two, have a different degree.
Graph schematic for L = 10 alongside adjacency matrix for L = 100 is provided. System sizes are coded by colour. a–f Anti-ferromagnetic order CAFM, XY order CXY, magnetisation density \(\langle {\hat{S}}^{z}\rangle /L\), von-Neumann entanglement entropy between sites V = 1. . . L/2 and V = L/2 + 1. . . L and Shannon-Entropy of the z−z and x−x correlations (see the “Methods” section) versus Δ. We use n = 256 bins to calculate the Shannon Entropy. Power-law curves have been fitted to CAFM and CXY for Δ > 2 and L = 120 and marked in green. A dotted red line has been added to plot e) to indicate the maximum possible value for the Shannon Entropy with the number of bins used.
