Levy-Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo

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The constrained-search principle introduced by Levy and Lieb, is proposed as a practical, though conceptually rigorous, link between Density Functional Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol realizes in practice the implicit key statement of DFT: "Given the three dimensional electron density of the ground state of a system of N electrons with external potential v(r) it is possible to find the corresponding 3N-dimensional wavefunction of ground state." From a numerical point of view, the proposed protocol can be employed to speed up the QMC procedure by employing DFT densities as a pre-selection criterion for the sampling of wavefunctions.