The Singular Euler-Maclaurin expansion on finite crystals

In this work, we show how boundary effects in long-range interacting lattice systems can be efficiently computed. We generalize the recently developed Singular Euler-Maclaurin expansion to crystals with boundaries, where the lattice contribution on top of the integral approximation is given in terms of truncated Epstein zeta functions. We present a new, exponentially convergent algorithm for the computation of the arising truncated Epstein zeta functions, and apply our approach to several physically relevant examples.