Fig. 2: Convergence of the AF conductivity for v − SiO₂ with respect to the broadening η for the Dirac δ, for a 192-atom model (left), for a 1536-atom model (center), and for a 5184-atom model (right).

Every dashed-red line is a Lorentzian having FWHM 2η, every solid-black line is a Gaussian with variance η²π/2 (both distributions have the same maximum (πη)⁻¹). Top row: evaluating the AF conductivity using the q interpolation and the Gaussian broadening yields a `convergence plateau', i.e., range of value for η for which the conductivity is not sensitive to the value of η (orange and blue lines show the converged `bulk' value for the AF conductivity at 100 and 300 K, respectively). The Gaussian yields a wider and more clear convergence plateau compared to the Lorentzian. Bottom row, calculations of the AF conductivity at q = 0: the small 192-atom model underestimates the bulk limit; in contrast, the medium 1536-atom model and the large 5184-atom model yield a convergence plateau also at q = 0, with the largest model featuring the widest convergence plateau. We note that the plateaus at q = 0 for the 1536- and the 5184-atom models are narrower than the corresponding ones obtained using the q interpolation. The vertical dotted lines are indicative of the minimum broadening for which computational convergence is achieved. The opposite trend of the broadening-conductivity curve obtained using the q mesh or q = 0 is discussed in Sec. Extension of the protocol to evaluate the anharmonic Wigner conductivity.