Ewald summation of multipolar interactions at an arbitrary order on a two‐dimensional lattice

There exist problems in condensed‐matter theory that require evaluating infinite Bloch sums of multipolar potential r−l−1Yl,m(θ,φ) on a periodic lattice. For an arbitrary multipolar order l, tractable formulas are given for summing such interactions on a two‐dimensional Bravais lattice and evaluating their Bloch sums at a point outside as well as inside the plane of the lattice. The approach used is the Ewald method, which consists of separating the original series in rapidly converging sums in reciprocal and real spaces. Computational aspects of the present formulation are briefly reviewed.