An automatic, high-order, adaptive algorithm for Brillouin zone integration

I will present a high-order, adaptive algorithm for Brillouin zone integration, applicable in the limit of small but non-zero broadening, and when the integrand can be evaluated on-the-fly using Wannier interpolation. The approach is significantly more efficient than other common adaptive integration strategies, as it has a mild polylogarithmic scaling with respect to the "broadening factor", or scattering rate, appearing in many standard Brillouin zone integrals. As a consequence, calculations with meV or sub-meV-scale broadening can be performed to several digits of accuracy with modest computational effort. The algorithm is high-order accurate, robust, black-box, and simple to implement, in particular for calculations on the irreducible Brillouin zone. I will demonstrate the practical performance of the method for a calculation of the density of states of the correlated metal SrVO3 with meV-scale broadening.