Quantum Monte Carlo(QMC) methods are accurate numerical tools used for computing the properties of physical models that contain a relatively large number of atoms, e.g.: crystals, nanoclusters or macromolecules. Although QMC computing time has the advantage of scaling with second or third powers of the system size, very precise results require the need to process large samples of phase space configurations and therefore the most challenging QMC problems require use of the most performant hardware and available algorithms .
In order to set the terminology we shall briefly describe the basic mathematical concepts that provide the foundation of QMC algorithms, for a more detailed presentation we direct the reader to Refs [3,4].
A typical quantum many-body system has electrons with positions , of which have spins up have spins down, and ions with positions . The particle interaction is described by the quantum Hamiltonian
QMC calculations can further improve a one particle solution by providing particle correlation contributions with the help of the following two QMC methods: