The triangular linear analytic method for two-dimensional spectral functions

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Abstract
A numerical scheme is presented for the calculation of two-dimensional Brillouin zone lattice spectra. The method is based on the subdivision of the irreducible part of the first Brillouin zone into triangular subcells, within which the energy eigenvalues and matrix elements are linearly interpolated. Analytic expressions are derived for both the real and the imaginary parts, including matrix elements, of a general lattice spectral function. As an illustration of the feasibility and computational ease of the method, the authors have calculated both the real and the imaginary parts of the lowest-order lattice Green functions for the s band of a nearest-neighbour tight-binding electronic system on a square lattice and found these to be in excellent agreement with well known analytic results. The method is also applied to the case of next-nearest-neighbour interactions where fewer analytic results are available.