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

TL;DR

This paper proposes a practical method linking Density Functional Theory and Quantum Monte Carlo via the Levy-Lieb principle, enabling more efficient wavefunction sampling using DFT densities.

Contribution

It introduces a numerical protocol based on the Levy-Lieb principle that connects DFT and QMC, improving sampling efficiency in quantum simulations.

Findings

The protocol can speed up QMC calculations.

DFT densities can be used as a pre-selection criterion.

The approach provides a rigorous link between DFT and QMC.

Abstract

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.