Simplex method for calculating two-particle spectral densities in two-dimensional interacting electron systems

In the theory of interacting two-dimensional (2D) electron systems, two-particle spectral densities defined as integrals over two independent wave vectors, constrained by a δ function, frequently occur. The numerical calculation of these spectral densities, formally 4D integrals constrained by a δ function, can be efficiently implemented by a generalization of the tetrahedron method, widely used in the 3D band-structure density-of-states calculation, to the four-dimensional case. We present the expressions needed to set up the 4D simplex density-of-states calculation, and give as an example the 4D free-electron band-structure density of states. © 1996 The American Physical Society.