Diffusion Monte Carlo

Diffusion Monte Carlo (DMC) or diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to calculate low-lying energies of a quantum many-body Hamiltonian. DMC is potentially numerically exact, meaning that it can find the exact ground state energy within a given error for any quantum system. When actually attempting the calculation, one finds that for bosons, the algorithm scales as a polynomial with the system size, but for fermions, DMC scales exponentially with the system size. This makes exact large-scale DMC simulations for fermions impossible; however, DMC employing a clever approximation known as the fixed-node approximation can still yield very accurate results.