A Recursive Hybrid Tetrahedron Method for Brillouin-zone Integration

TL;DR

This paper introduces a recursive hybrid tetrahedron method for Brillouin-zone integration that improves accuracy and handles multiple singularities, enhancing calculations of response and spectral functions in materials.

Contribution

It presents a novel recursive extension of the hybrid tetrahedron method, enabling iterative refinement and better handling of singularities in Brillouin-zone integrations.

Findings

Reduces integration error compared to linear tetrahedron method

Capable of handling multiple singularities simultaneously

Demonstrates improved convergence in practical calculations

Abstract

A recursive extension of the hybrid tetrahedron method for Brillouin-zone integration is proposed, allowing iterative tetrahedron refinement and significantly reducing the error from the linear tetrahedron method. The Brillouin-zone integral is expressed as a weighted sum on the initial grid, with integral weights collected recursively from the finest grid. Our method is capable of simultaneously handling multiple singularities in the integrand and thus may provide practical solutions to various Brillouin-zone integral tasks encountered in realistic calculations, including the computation of response and spectral function with superior sampling convergence. We demonstrate its effectiveness through numerical calculations of the density response functions of two model Hamiltonians and one real material system, the face-centered cubic cobalt.