Efficient calculation of high-order self-energy corrections to phonon linewidths: Application to α-nitrogen

This paper presents an efficient method for computing high-order corrections to phonon linewidths in crystals. Traditional algorithms involve nested sums over intermediate phonon states, whose computational time grows exponentially with the perturbation order. This nested-sum difficulty is overcome in the present study for the special case of the double-vertex diagrams by writing the corresponding linewidths in a simple form and exploiting a recursive algorithm for weighted phonon densities of states, which requires a time linear in the perturbation order. Using this method, we computed, up to order 10, the linewidths due to the double-vertex diagrams for the α-nitrogen crystal. Our calculation shows that accurate estimates of high-order linewidth corrections can be obtained even for systems as complex as molecular crystals.