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

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.Program summaryProgram title: SimTetCatalogue identifier: AEKF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKF_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3176No. of bytes in distributed program, including test data, etc.: 19 416Distribution format: tar.gzProgramming language: FortranComputer: Any computer with a Fortran compilerOperating system: Unix, Linux, WindowsRAM: 512 MbytesClassification: 4.11, 7.3Nature of problem: The integration of the Greenʼs function over the Brillouin zone appears in the computations of many physical quantities in solid-state physics.Solution method: The integral over the Brillouin zone is computed with the tetrahedron linear method. The complex weights are generated with the novel algebraic formulas free of apparent singularities and well suited for automatic computations.Running time: A few μsec per integral.

► Integral over the tetrahedron.
► Analytical properties of the integrand function on the complex plane.
► The integral solution in the form suitable for the automatic computation.