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We present a method for calculating the complex Green function $G_{ij}(\omega)$ at any real frequency $\omega$ between any two sites $i$ and $j$ on alattice. Starting from numbers of walks on square, cubic, honeycomb,triangular, bcc, fcc, and diamond lattices, we derive Chebyshev expansioncoefficients for $G_{ij} (\omega)$. The convergence of the Chebyshev series canbe accelerated by constructing functions $f(\omega)$ that mimic the van Hovesingularities in $G_{ij} (\omega)$ and subtracting their Chebyshev coefficientsfrom the original coefficients. We demonstrate this explicitly for the squarelattice and bcc lattice. Our algorithm achieves typical accuracies of 6--9significant figures using 1000 series terms.

A general method for calculating lattice Green functions on the branch cut