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

Abstract

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 a lattice. Starting from numbers of walks on square, cubic, honeycomb, triangular, bcc, fcc, and diamond lattices, we derive Chebyshev expansion coefficients for $G_{ij}(\omega )$. The convergence of the Chebyshev series can be accelerated by constructing functions $f(\omega )$ that mimic the van Hove singularities in $G_{ij}(\omega )$ 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.

12 pages, 6 figures, 6 tables

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Elliptic integral evaluations of Bessel moments
• A Fast Approach to Creative Telescoping
• Green's function on lattices
• Bias-free simulation of diffusion-limited aggregation on a square lattice

Cited by in corpus (1)

• Exceptional Lattice Green's Functions