Renormalization method for infinite lattice sums revisited: lattice sums with Bloch phase factor

TL;DR

This paper extends a renormalization-based method to efficiently evaluate infinite lattice sums with Bloch phase factors, improving accuracy control and applicability to periodic systems.

Contribution

It generalizes the renormalization scheme to include Bloch phase factors, enabling accurate and fast calculations for long-range interactions in periodic lattices.

Findings

The method is fast and easily controllable in accuracy.

It is applicable to any points in the Brillouin zone.

Illustrative calculations demonstrate its effectiveness.

Abstract

Infinite lattice summation scheme based on the idea of renormalization is generalized to enable evaluation of infinite lattice sums with Bloch phase factors which can occur when treating long-range interactions in infinite periodic systems. The scheme is fast, with easy to control accuracy and is not limited to any choice of special points in the Brillouin zone. Illustrative calculation for a first few contributions for a simple cubic lattice is presented.