Metropolis (Markov Chain) Monte Carlo methods (MCMC) have been used for the past 70 years to “solve” for equilibrium properties of classical many-body systems. At the same time Feynman introduced an imaginary time path integral formalism which allows for solution of the equilibrium calculation of certain quantum systems, namely bosons, bolzmannons, and fermions in 1 dimension. A more specialized algorithm, projector MC, (also known as Diffusion Monte Carlo) can be used to calculate properties single states of fermion systems within a variational approximation. These and other related algorithms will be briefly introduced.
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