Abstract
We present a method for calculating the complex Green function at any real frequency ω between any two sites i and j on a lattice. Starting from numbers of walks on square, cubic, honeycomb, triangular, bcc, fcc, and diamond lattices, we derive Chebyshev expansion coefficients for . The convergence of the Chebyshev series can be accelerated by constructing functions that mimic the van Hove singularities in and subtracting their Chebyshev coefficients from the original coefficients. We demonstrate this explicitly for the square lattice and bcc lattice. Our algorithm achieves typical accuracies of 6–9 significant figures using 1000 series terms.
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