Between Classical and Quantum Monte Carlo Methods: “Variational” QMC

The variational Monte Carlo method is reviewed here. It is in essence a classical statistical mechanics approach, yet allows the calculation of quantum expectation values. We give an introductory exposition of the theoretical basis of the approach, including sampling methods and acceleration techniques; its connection with trial wavefunctions; and how in practice it is used to obtain high quality quantum expectation values through correlated wavefunctions, correlated sampling, and optimization. A thorough discussion is given of the different methods available for wavefunction optimization. Finally, a small sample of recent works is reviewed, giving results and indicating new techniques employing variational Monte Carlo.