Past and recent progress of the variational approach by quantum Monte Carlo

I review the most simple, but in my opinion most powerful, technique to describe the electron correlation in realistic materials, the nowadays standard Variational Monte Carlo method. I report several progress in this field [1], that cover two main achievements, developed in the last decades: i) the possibility to optimize stochastically the energy of a highly accurate many-body wave function, described by several variational parameters, ii) the development of the so called Jastrow Mean-Field ansatz that will be shown to be extremely accurate and nevertheless computationally feasible even for large scale electronic structure applications, especially in recent high-performance supercomputers.

[1] 7045 K. Nakano et al. "TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo", J. Chem. Phys. 152, 204121 (2020); https://doi.org/10.1063/5.0005037

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