Linear-scaling methods have paved the way for large-scale ab initio calculations of solid-state systems. Existing methods suffer from two well-known limitations. First, they are only applicable to sparse systems, i.e., when long-range orbital interactions exponentially decay and therefore the Hamiltonian matrices have a small number of non-zero elements. Second, their computational performance is negatively impacted when high accuracy is needed. In this work, by revisiting linear scaling kernels, we introduce a new approach with nearly-linear complexity, provable convergence properties, and global applicability even for dense systems. We demonstrate their advantages and limitations both in theory and in practice.

Towards provably accurate and globally applicable linear-scaling ab initio methods

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