EFFICIENT CALCULATION OF HIGH-ORDER SELF-ENERGY CORRECTIONS TO PHONONLINEWIDTHS - APPLICATION TO ALPHA-NITROGEN

This paper presents an efficient method for computing high-order corre ctions to phonon linewidths in crystals. Traditional algorithms involv e nested sums over intermediate phonon states, whose computational tim e grows exponentially with the perturbation order. This nested-sum dif ficulty is overcome in the present study for the special case of the d ouble-vertex diagrams by writing the corresponding linewidths in a sim ple form and exploiting a recursive algorithm for weighted phonon dens ities of states, which requires a time linear in the perturbation orde r. Using this method, we computed, up to order 10, the linewidths due to the double-vertex diagrams for the a-nitrogen crystal. Our calculat ion shows that accurate estimates of high-order linewidth corrections can be obtained even for systems as complex as molecular crystals.