Stochastic vector computational approaches for the electronic structure of extended condensed matter systems help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. The electronic density is estimated by a stochastic process that samples the Kohn-Sham eigenstate contribution according to the Fermi Dirac occupation, completely avoiding the actual calculation of eigenstates. We also discuss post-DFT stochastic methods, such as the G0W0 approximation for quasiparticle energies.
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