(a) Diagonal and (b) off-diagonal (for ) matrix elements of the nearest-neighbor spin correlations for the ferromagnetic transverse-field Ising model () in two dimensions [14, 15]. Continuous lines in (b) depict running averages. The inset in (a) shows that the fluctuations of the diagonal matrix elements are different in the two sectors shown. Inset in (b): ratio between the running averages of the off-diagonal matrix elements. The dashed line shows that, as expected from the ETH [6, 19], the ratio is very close to the square root of the inverse ratio between the Hilbert space dimension of the sectors. , , , are the eigenvalues of the spin-flip, mirror-, mirror-, and mirror along the line symmetries, respectively. The results shown are for the zero momentum sector of a lattice with sites (see Ref. [15] for further details).