High-order and adaptive optical conductivity calculations using Wannier interpolation

TL;DR

This paper introduces an automatic, high-order adaptive Brillouin zone integration algorithm for calculating optical conductivity with small broadening, leveraging Wannier interpolation for efficient and accurate results in first-principles calculations.

Contribution

The authors develop a novel adaptive integration method that achieves high accuracy and efficiency in optical conductivity calculations using Wannier interpolation, automating convergence testing.

Findings

Successfully resolves Drude and interband peaks with sub-meV broadening.

Achieves polylogarithmic computational complexity with respect to broadening parameter.

Demonstrates automated convergence testing for first-principles transport calculations.

Abstract

We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity with a non-zero but small broadening factor $\eta$, focusing on the case in which a Hamiltonian in a downfolded model can be evaluated efficiently using Wannier interpolation. The algorithm uses iterated adaptive integration to exploit the localization of the transport distribution near energy and energy-difference iso-surfaces, yielding polylogarithmic computational complexity with respect to $\eta$. To demonstrate the method, we compute the AC optical conductivity of a three-band tight-binding model, and are able to resolve the Drude and interband peaks with broadening in the sub-meV regime to several digits of accuracy. Our algorithm automates convergence testing to a user-specified error tolerance, providing an important tool in black-box first-principles calculations of electrical transport phenomena and other response functions.