AutoBZ.jl: An Open-Source Library for Automatic and Adaptive Brillouin Zone Integration

Brillouin zone integration is a standard operation in electronic structure calculations used to compute a wide range of physical observables. For systems at finite temperature with a significant scattering rate, represented by a large broadening factor $eta$, standard equispaced integration methods are highly effective. However, when the broadening $eta$ is small, adaptive methods become necessary to achieve converged results. The AutoBZ.jl library introduces both generic and specialized integration routines implementing automatic, optimized, and high-order accurate methods for integrals, with both large and small broadening, using Wannier interpolation. The package automatically selects the suitable integration routine for a given system and is optimized to use the irreducible Brillouin zone based on crystal symmetries. Written in Julia, the library is both extensible and performant, interfaces with Python, and obtains the ab-initio Hamiltonian as standard output of Wannier90. Code examples are demonstrated using calculations of the density of states and optical conductivity of the correlated metal SrVO$_3$ with broadening down to the sub-meV scale.