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.
Keywords: Condensed Matter - Materials Science
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