Reduced-scaling many-body electronic structure: old ideas that really work.
I will review recent progress in reduced-scaling electronic structure methodology. Many-body electronic structure methods, like coupled-cluster in chemistry and Green's function methods in solid state physics, are capable of significantly higher accuracy than the density functional theory, but their application is hindered by their significantly higher computational cost. Recent rapid advances in reduced-scaling formulation of the coupled-cluster and other many-body theories, in combination with numerical regularization of Coulomb Hamiltonian singularities, reduces or eliminates the cost gap between the many-body methodology and DFT. I will review the key ideas (most of them quite old) behind the modern reduced-scaling electronic structure methods that allow to expose and utilize the sparsity of the electronic wave function, and discuss some of our recent work in this area.