Quantum Monte Carlo
| Electronic structure methods |
|---|
| Valence bond theory |
|
Coulson–Fischer theory Generalized valence bond Modern valence bond theory |
| Molecular orbital theory |
|
Hartree–Fock method Semi-empirical quantum chemistry methods Møller–Plesset perturbation theory Configuration interaction Coupled cluster Multi-configurational self-consistent field Quantum chemistry composite methods |
| Density functional theory |
|
Time-dependent density functional theory Thomas–Fermi model Orbital-free density functional theory Adiabatic connection fluctuation dissipation theorem Görling-Levy pertubation theory Optimized effective potential method Linearized augmented-plane-wave method Projector augmented wave method |
| Electronic band structure |
|
Nearly free electron model Tight binding Muffin-tin approximation k·p perturbation theory Empty lattice approximation GW approximation Korringa–Kohn–Rostoker method |
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem.
Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.