An algebraic formulation and implementation of the tetrahedron linear method for the Brillouin zone integration of spectral functions Original Research Article

A package of FORTRAN subroutines is provided for the Brillouin zone (BZ) integration of the Greenʼs functions (GF) and spectral functions. The relevant weighting factors at sampling points in the BZ are evaluated to high precision with the help of the formulas for both the real and imaginary parts. The analytical properties of implemented expressions are discussed, and their range of validity is determined. The limiting cases when values at the tetrahedron corners coincide are worked out in terms of the finite difference quotients and replaced by the derivatives. The present numerical algorithms are developed for one-, two- and three-dimensional simplexes, with the potential ability of handling simplexes with higher dimensions as well. As an example, the results of computation the simple cubic lattice GFʼs are presented.